"Handlers" are also called "Action" classes. They are used in web applications that employ a "model 2" (also called model-view-controller, MVC) design
pattern.
A "model 2" web app has what's called a controller
servlet whose sole responsibilty to receive http requests from web browsers, determine what the end-user wants to do, determine which class is designed to execute the user's request, and calls a method on that class to
handle that
action.
My impression is that the term "Handler" is what developers called these classes in the pre-internet client-server days. They are now called "Actions".
Simon Brown has an excellent chapter in his book "Servlets 2.3" about designing web applications and you can download it for free on his web site
http://www.simongbrown.com.