Merge is an overloaded word. There is a content merge and then there is a branch merge. A content merge is where you have edited a file and someone checked in a newer file, so the source control system will tell you to do a content merge before checking in the file (if it's interactive, it's a 3-way merge GUI).

A branch merge is migrating changes from one branch to another. If a source branch A has a file rock.cs that had been edited and file scissors.cs that had been deleted, merging these changes into a target branch B would result in a pending edit on file rock.cs and a pending delete on the file scissors.cs in the target.

Here's a simple example that uses the command line.  The biggest differences between this and a “real-world“ example are the number of files involved (you may have thousands) and that you would probably have conflicts for a subset of the files (e.g., the same file was edited both in the source and in the target, resulting in the need to do a 3-way content merge).

The /i option is the shortcut for the "noprompt" option that makes everything non-interactive, as would be needed in batch script. Changes are committed in change sets, and the whole check in either succeeds or fails (it's atomic).

1. Create a workspace and add the files mentioned in the merge explanation above. 

D:\project>h workspace /i /new MyProject

D:\project>h add /r A
A

A:
rock.cs
scissors.cs

D:\project>h checkin /i
add A

A:
add rock.cs
add scissors.cs
Change set #4 checked in.
2. Create a branch from A to a target B. 
D:\project>h branch A B
B

B:
rock.cs
scissors.cs

D:\project>h checkin /i
branch B

B:
branch rock.cs
branch scissors.cs
Change set #5 checked in.
3. Now we have A and B in the repository, related by B being a branch of A. 
D:\project>h dir /r
$/:
$A
$B

$/A:
rock.cs
scissors.cs

$/B:
rock.cs
scissors.cs

6 item(s)
4. The branches command shows that B is branched from A. 
D:\project>h branches A
>> $/A <<
     $/B Branched from version 1
5. Now we edit rock.cs and delete scissors.cs in the source branch. 
D:\project>h edit A\rock.cs
A:
rock.cs

D:\project>echo new line >> A\rock.cs

D:\project>h delete A\scissors.cs
A:
scissors.cs

D:\project>h checkin /i
A:
edit rock.cs
delete scissors.cs
Change set #6 checked in.
6. Merge the changes made in branch A over to branch B. Of course in a real project, there may be conflicts to resolve (rock.cs may have been edited both in the source and target, which will need to be merged with a 3-way content merge), and the developer may need to make additional changes in B (for example, B may be a newer release of the project and the code may be need to be changed due to an API change made earlier in B). 
D:\project>h merge A B
merge, edit: $/A/rock.cs;C5~C6 -> $/B/rock.cs;C5
merge, delete: $/A/scissors.cs;C5~C6 -> $/B/scissors.cs;C5

D:\project>h checkin /i
B:
merge, edit rock.cs
merge, delete scissors.cs
Change set #7 checked in.
6. In the history, we see that B\rock.cs was created by branching in change set 5 and then an edit was merged in change set 7. 
D:\project>h history /i B\rock.cs
Vers Date       Chngset User          Change Type          Files
---- ---------- ------- ------------- -------------------- --------------------
   2 06/14/2004       7 buckh         merge, edit          $/B/rock.cs
   1 06/14/2004       5 buckh         branch               $/B/rock.cs