Using ASP.NET Web API, we can build scalable HTTP services which can serve wide range of client application\devices.

I am using the sample from Mike Wasson to look at some of the internals
http://www.asp.net/web-api/overview/getting-started-with-aspnet-web-api/tutorial-your-first-web-api

I attached windbg to the server process (in this case, w3wp.exe) and loaded sos. For information on how to use the debugger and\or SOS\Psscor OR other extensions that are available, I will recommend to look at either Tess's Blog OR other online resources (there are plenty of them)

There are various other approaches to take to look at these objects and this blog is just one of the ways to understand how all these co-relate in the memory

Lets look at how the ApiExplorer object looks like,
0:018> !do 0000002ce24df088
Name:        System.Web.Http.Description.ApiExplorer
MethodTable: 000007f8f77d6a60
EEClass:     000007f8f77f23e0
Size:        40(0x28) bytes
File:        C:\Windows\Microsoft.NET\Framework64\v4.0.30319\Temporary ASP.NET Files\hellowebapi\1b80443e\ce29f4de\assembly\dl3\0065a2d0\2cd0f544_4a85cd01\System.Web.Http.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f8f77daf30  4000032        8 ...ttp]], mscorlib]]  0 instance 0000002ce24df0f0 _apiDescriptions
000007f8f7735dc8  4000033       10 ...HttpConfiguration  0 instance 0000002ce24dcd98 _config
....

Lets look at how it was configured,
0:018> !do 0000002ce24dcd98
Name:        System.Web.Http.HttpConfiguration
MethodTable: 000007f8f7735dc8
EEClass:     000007f8f77c02c0
Size:        104(0x68) bytes
File:        C:\Windows\Microsoft.NET\Framework64\v4.0.30319\Temporary ASP.NET Files\hellowebapi\1b80443e\ce29f4de\assembly\dl3\0065a2d0\2cd0f544_4a85cd01\System.Web.Http.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f8f7737338  4000211        8 ...tpRouteCollection  0 instance 0000002ce24dca60 _routes
000007f95af8c688  4000212       10 ...bject, mscorlib]]  0 instance 0000002ce24dce78 _properties
000007f8f773a600  4000213       18 ...rmatterCollection  0 instance 0000002ce24dd148 _formatters
000007f8f7586618  4000214       20 ...System.Net.Http]]  0 instance 0000002ce24deca0 _messageHandlers
000007f8f773b1c0  4000215       28 ...pFilterCollection  0 instance 0000002ce24ded08 _filters
000007f8f773b668  4000216       30 ...ependencyResolver  0 instance 0000002ce24ded68 _dependencyResolver
000007f8f773b850  4000217       38 ...System.Web.Http]]  0 instance 0000002ce24ded80 _initializer
000007f8f7586c18  4000218       40 ...sable, mscorlib]]  0 instance 0000002ce24dedc0 _resourcesToDispose
000007f955e3c7b8  4000219       5c       System.Boolean  1 instance                0 _disposed
000007f8f7737b80  400021a       48 ...ServicesContainer  0 instance 0000002ce24dee08 <Services>k__BackingField
000007f8f773be68  400021b       50 ...ngRulesCollection  0 instance 0000002ce24e06e0 <ParameterBindingRules>k__BackingField
000007f8f7735c70  400021c       58         System.Int32  1 instance                0 <IncludeErrorDetailPolicy>k__BackingField

Lets look at the route,
0:018> !do 0000002ce24dca60
Name:        System.Web.Http.WebHost.Routing.HostedHttpRouteCollection
MethodTable: 000007f8f77375f8
EEClass:     000007f8f77c0a70
Size:        56(0x38) bytes
File:        C:\Windows\Microsoft.NET\Framework64\v4.0.30319\Temporary ASP.NET Files\hellowebapi\1b80443e\ce29f4de\assembly\dl3\aaff774c\120cf144_4a85cd01\System.Web.Http.WebHost.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f955e3aee0  400007b        8        System.String  0 instance 0000002ce24dcd78 _virtualPathRoot
000007f8f7738630  400007c       10 ...System.Web.Http]]  0 instance 0000002ce24dcab8 _collection
000007f8f7738d70  400007d       18 ...System.Web.Http]]  0 instance 0000002ce24dcb20 _dictionary
000007f955e3c7b8  400007e       20       System.Boolean  1 instance                0 _disposed
000007f954ede2e0  400007a       b8           System.Uri  0   static 0000002ce24dcbb0 _referenceBaseAddress
000007f94ba16050  4000014       28 ...g.RouteCollection  0 instance 0000002ce24dc328 _routeCollection
0000000000000000  4000015       50                       0   static 0000000000000000 CS$<>9__CachedAnonymousMethodDelegate1

0:018> !do 0000002ce24dc328
Name:        System.Web.Routing.RouteCollection
MethodTable: 000007f94ba16050
EEClass:     000007f94b64f180
Size:        64(0x40) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\System.Web\v4.0_4.0.0.0__b03f5f7f11d50a3a\System.Web.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f9557bb470  4000c7b        8 ...Canon, mscorlib]]  0 instance 0000002ce24dc418 items
..

0:018> !do 0000002ce24dc418
Name:        System.Collections.Generic.List`1[[System.Web.Routing.RouteBase, System.Web]]
MethodTable: 000007f94b5932b0
EEClass:     000007f9558512a8
Size:        40(0x28) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f955e1f1b8  4000c6c        8      System.Object[]  0 instance 0000002ce24e2438 _items
000007f94b592fb8  40014d8       18 ...ase, System.Web]]  0 instance 0000002ce24dc368 _namedMap
..

0:018> !da -details 0000002ce24e2438
Name:        System.Web.Routing.RouteBase[]
MethodTable: 000007f955e1f1b8
EEClass:     000007f955851858
Size:        64(0x40) bytes
Array:       Rank 1, Number of elements 4, Type CLASS
Element Methodtable: 000007f94ba15068
[0] 0000002ce24e1c38
    Name:        System.Web.Http.WebHost.Routing.HttpWebRoute
    MethodTable: 000007f8f7821098
    EEClass:     000007f8f77f7318
    Size:        80(0x50) bytes
    File:        C:\Windows\Microsoft.NET\Framework64\v4.0.30319\Temporary ASP.NET Files\hellowebapi\1b80443e\ce29f4de\assembly\dl3\aaff774c\120cf144_4a85cd01\System.Web.Http.WebHost.dll
    Fields:
                      MT    Field   Offset                 Type VT     Attr            Value Name
        000007f955e3aee0  40014d1       10            System.String      0     instance     0000002ce24e0af0     _url
..
[1] 0000002ce24e2728
    Name:        System.Web.Mvc.RouteCollectionExtensions+IgnoreRouteInternal
    MethodTable: 000007f94af9e988
    EEClass:     000007f94adb6380
    Size:        72(0x48) bytes
    File:        C:\Windows\Microsoft.Net\assembly\GAC_MSIL\System.Web.Mvc\v4.0_4.0.0.0__31bf3856ad364e35\System.Web.Mvc.dll
    Fields:
                      MT    Field   Offset                 Type VT     Attr            Value Name
        000007f955e3aee0  40014d1       10            System.String      0     instance     0000002ce24e2610     _url
  ..
[2] 0000002ce24e2ac8
    Name:        System.Web.Routing.Route
    MethodTable: 000007f94ba14e18
    EEClass:     000007f94b64e530
    Size:        72(0x48) bytes
    File:        C:\Windows\Microsoft.Net\assembly\GAC_64\System.Web\v4.0_4.0.0.0__b03f5f7f11d50a3a\System.Web.dll
    Fields:
                      MT    Field   Offset                 Type VT     Attr            Value Name
        000007f955e3aee0  40014d1       10            System.String      0     instance     0000002ce24e2688     _url
...

0:018> !do 0000002ce24e0af0    
Name:        System.String
MethodTable: 000007f955e3aee0
EEClass:     000007f9557a3720
Size:        68(0x44) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
String:      api/{controller}/{id}
which is the route for DefaultApi

0:018> !do 0000002ce24e2610    
Name:        System.String
MethodTable: 000007f955e3aee0
EEClass:     000007f9557a3720
Size:        78(0x4e) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
String:      {resource}.axd/{*pathInfo}

0:018> !do 0000002ce24e2688    
Name:        System.String
MethodTable: 000007f955e3aee0
EEClass:     000007f9557a3720
Size:        78(0x4e) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
String:      {controller}/{action}/{id}
Which is the route for default

We can also confirm this through _namedMap Dictionary,
0:018> !do 0000002ce24dc368
Name:        System.Collections.Generic.Dictionary`2[[System.String, mscorlib],[System.Web.Routing.RouteBase, System.Web]]
MethodTable: 000007f94b592fb8
EEClass:     000007f955851e10
Size:        80(0x50) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f955e3dc30  4000c3f        8       System.Int32[]  0 instance 0000002ce24e2478 buckets
000007f955e9b488  4000c40       10 ...non, mscorlib]][]  0 instance 0000002ce24e24a0 entries
000007f955e3dc90  4000c41       38         System.Int32  1 instance                2 count
000007f955e3dc90  4000c42       3c         System.Int32  1 instance                2 version
..

0:018> !da -details 0000002ce24e24a0
Name:        System.Collections.Generic.Dictionary`2+Entry[[System.String, mscorlib],[System.Web.Routing.RouteBase, System.Web]][]
MethodTable: 000007f94c40a888
EEClass:     000007f94b66de90
Size:        96(0x60) bytes
Array:       Rank 1, Number of elements 3, Type VALUETYPE
Element Methodtable: 000007f94c401090
[0] 0000002ce24e24b0
    Name:        System.Collections.Generic.Dictionary`2+Entry[[System.String, mscorlib],[System.Web.Routing.RouteBase, System.Web]]
    MethodTable: 000007f94c401090
    EEClass:     000007f955857ee8
    Size:        40(0x28) bytes
    File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
    Fields:
                      MT    Field   Offset                 Type VT     Attr            Value Name
 ...
        000007f955e40120  4000c4f        0           System.__Canon      0     instance     0000002ce24e0ac0     key
        000007f955e40120  4000c50        8           System.__Canon      0     instance     0000002ce24e1c38     value
[1] 0000002ce24e24c8
    Name:        System.Collections.Generic.Dictionary`2+Entry[[System.String, mscorlib],[System.Web.Routing.RouteBase, System.Web]]
    MethodTable: 000007f94c401090
    EEClass:     000007f955857ee8
    Size:        40(0x28) bytes
    File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
    Fields:
                      MT    Field   Offset                 Type VT     Attr            Value Name
        ...
        000007f955e40120  4000c4f        0           System.__Canon      0     instance     0000002ce24e2660     key
        000007f955e40120  4000c50        8           System.__Canon      0     instance     0000002ce24e2ac8     value

First Key\Value pair,

0:018> !do 0000002ce24e0ac0    
Name:        System.String
MethodTable: 000007f955e3aee0
EEClass:     000007f9557a3720
Size:        46(0x2e) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
String:      DefaultApi

0:018> !do 0000002ce24e1c38    
Name:        System.Web.Http.WebHost.Routing.HttpWebRoute
MethodTable: 000007f8f7821098
EEClass:     000007f8f77f7318
Size:        80(0x50) bytes
File:        C:\Windows\Microsoft.NET\Framework64\v4.0.30319\Temporary ASP.NET Files\hellowebapi\1b80443e\ce29f4de\assembly\dl3\aaff774c\120cf144_4a85cd01\System.Web.Http.WebHost.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f955e3c7b8  40014d0        8       System.Boolean  1 instance                1 _routeExistingFiles
000007f955e3aee0  40014d1       10        System.String  0 instance 0000002ce24e0af0 _url
..

0:018> !do 0000002ce24e0af0
Name:        System.String
MethodTable: 000007f955e3aee0
EEClass:     000007f9557a3720
Size:        68(0x44) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
String:      api/{controller}/{id}

Second key\Value pair,
0:001> !do -nofields 0000002ce24e2660    
Name:        System.String
MethodTable: 000007f955e3aee0
EEClass:     000007f9557a3720
Size:        40(0x28) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
String:      Default

0:001> !do 0000002ce24e2ac8    
Name:        System.Web.Routing.Route
MethodTable: 000007f94ba14e18
EEClass:     000007f94b64e530
Size:        72(0x48) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\System.Web\v4.0_4.0.0.0__b03f5f7f11d50a3a\System.Web.dll
Fields:
              MT    Field   Offset                 Type VT     Attr            Value Name
000007f955e3aee0  40014d1       10        System.String  0 instance 0000002ce24e2688 _url
..

0:001> !do 0000002ce24e2688
Name:        System.String
MethodTable: 000007f955e3aee0
EEClass:     000007f9557a3720
Size:        78(0x4e) bytes
File:        C:\Windows\Microsoft.Net\assembly\GAC_64\mscorlib\v4.0_4.0.0.0__b77a5c561934e089\mscorlib.dll
String:      {controller}/{action}/{id}