According to this Irelia guide, if you cancel the animation early then your next auto-attack will start sooner (I could be interpreting it wrong – it could simply mean that staying close to your opponent will allow you to do more damage).
Basically put, the auto attack animation will apply damage before it is fully finished, so you can cancel it halfway through, move up a little, and reactivate the auto attack. It is difficult to master, but once you do learn it, you can attack 3 times in what would normally be 2.
My question is, can you effectively increase your attack speed with AA animation cancelling? If you time the animation cancel right by moving in between autos, can you attack faster? As a dedicated AD Carry player, I feel like I should know this by now.
Note: For info on what animation cancelling is, see this page.
Best Answer
Your entire attack animation consists of three different kinds of frames: your initial swing, the hit, and the backswing. Animation cancelling consists of cancelling the backswing portion of the animation, usually by moving, to get in to a better position to continue attacking.
Keep in mind though, even though you cancel the backswing, there's still a built in-cooldown before you can attack again that's identical whether or not you choose to cancel. The main advantage, as well as the point trying to be made in the Irelia guide, is that by cancelling it allows you to reposition more aggressively(move forward) so that if a champion was retreating that can result in additional attacks.
Certain champs can cancel in to skills to effectively "double" their auto-attacks though since it resets their auto-attack cooldown, such as Sivirs bouncing blades, or Jax's Empower. Effective use of this is very important to maximize damage.