This is the publish/subscribe pattern. Some element "publishes" notices of the occurrences of events that reflect changes in its state. Other elements register an intent to receive notification about these events, i.e., they "subscribe." This is also called "event-listening," and handlers are often referred to as "listeners."
The keyboard, pointing device (mouse, touch-pad, etc.), form elements, window - all of these items and more - publish a wide variety of events without your having to do anything. For instance, onmouse* events, onchange, onclick, onkeypress are standard events published for a wide variety of elements. In order to subscribe, you register a handler. That is, you declare that a function should be called whenever a particular event is published by a particular element.
"Handler" is simply the common term applied to these functions. The handler can do anything you find appropriate in response to receiving notification of the event.
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Here's a couple of samples, one with the YUI class you were wrestling, one without.