There are a couple types of cancels in play in MK9:
1) Actually cancelling something. Like with Kitana's EX fan, you can cancel the second throw of it completely by holding 1 and dashing out of it. Same with Jax's ground pound -- you can stop it before it completes, which allows you to move or so something else. Same with Kabal's nomad dash -- you can stop it before he actually dashes across the screen.
So in these cases, you allow the move to start up, and then stop it cold so you can do something else.
2) Interrupting one thing with another. This is where you start a new input before the frames of the previous one would have ended. There are normals that can be interrupted by specials, dashes than can be interrupted by normals or block, etc.
As for the second one, one of the primary reasons it's useful is that it allows you to modify the properties of certain moves and strings. For example, if I hit an opponent with a move that is negative on block, and he blocks it, he'd normally recover before I do -- so he'd be able to start pressure on me, or even punish if the window is large enough. However, by cancelling that move before it ends into another move that is safe on block, the disadvantage is removed when the first move is interrupted early by the second.
This can lead to mindgames, because it can prevent people from being able to interrupt your offense in certain spots, or prevent them from being able to counterattack when they normally would.
In general, cancelling can be used for all kinds of things, from baiting opponents into making mistakes, to extending combos, to building meter.
