Handle custom URL portion after /

I am honestly not sure what it is called, however hopefully someone here knows how and what exactly it is.

I want to be able to handle a URL sent to my server, and display different site based on the URL. Such as facebook and twitter do, (i.e. facebook.com/usernamehere) I assume that the server takes that link and parses to load the right information based on the URL, but I am not exactly sure what that is called or how I can achieve that effect.