Focus scopes are a mechanism in avalon for allowing multiple elements to have focus simultaneously.  A very common example of multiple focus can be seen in Word - say you want to change the font size of a selection of text.  You select the text, then start typing in the font control to change the font size - and the application remembers that the text itself was selected.  If you built this kind of application in avalon without setting up focus scopes, the original textbox would lose focus when you started typing in the font size.

Here's a very simple example of a xaml layout with multiple focus scopes:

<StackPanel>
 <TextBox/>
 <TextBox FocusManager.IsFocusScope="True"/>
</StackPanel>

If you type some text into the first textbox, and select it, you can then give focus to the second text box without the original losing focus.  The avalon terminology is "logical" vs. "keyboard" focus - the original text box has logical focus, while the second text box would have keyboard focus. 

Also note that any elements that are in one focus scope won't lose logical focus if the keyboard focus changes to target an element in another focus scope.  In other words, every focus scope can have an element with logical focus, but only one element in the entire tree will have keyboard focus.