Jenkins classes are bound to URLs by using Stapler.
The singleton Jenkins instance is bound to the context root (most of the time "/") URL, and the rest of the objects are bound according to their reachability from this root object.
Stapler uses reflection to recursively determine how to process any given URL.
A few examples of how the URL /foo/bar could be processed:
A getFoo(String) is defined on the Jenkins object, and Stapler passes bar as a parameter.
The object returned has a method called doIndex(…) that gets called and renders the response.
getFoo() is defined and returns an object that has a getBar or doBar method.
The object returned from that has an associated index.jelly or index.groovy view.
getFoo() is are defined and the returned object has a view named bar.jelly or bar.groovy defined.
doFoo() is defined.
A number of additional ways to handle requests exist, but these are the most common.