Basically it's a mechanism to notify objects that something has happened. When you dispatch an event, something needs to be listening for that event.
It's basically like making a telephone call ( dispatchEvent(new CallEvent(CallEvent.CALL)) ). If the person you are trying to ring isn't in, they aren't listening to the telephone event, so they can't do anything about it. If they are in ( addEventListener(CallEvent.Call, answerHandler) ), they can answer it, maybe send it straight to voice mail.
For a full rundown, try reading this article from adobe.
http://www.adobe.com/devnet/actionscript/articles/event%5Fhandling%5Fas3%5F02.html
A lot of programming languages make use of events so it's very worth while getting to grips with it.
James
Response to Edit1
It looks to me like you have a method that has been set up to handle a MouseEvent.Click on some object somewhere. When that happens it sets another objects scaleX property to 0 (making it invisible). A new Event is then Dispatched with the type set to "setVolume". This on it's own wouldn't do anything. Somewhere else this is probably a line looks a little like addEventListener("setVolume", doSomethingMethod); . When the original method is fired (seemingly a mouse click), the doSomethingMethod should fire.