It's a game mechanic that takes many hours of practice to perfect, but is it worth it to learn if you're hardly using the AD carries in LoL?
Sort of a tangent, but if you plan to successfully climb the solo queue ladder, you will have to play AD carries. Not to mention that understanding the aspects of all lanes is essential regardless of which role you fill.
Animation cancelling is more prevalent in other games such as StarCraft:BW and DOTA, but it is still useful in LoL. Basically it will reduce predictability in lane when you're last hitting as a ranged champion (generally mid and bot) as you're standing still for a fraction of the original animation time.
Personally, I come from a SC:BW background and animation cancelling is second nature so I didn't have to spend time practicing it, however all it takes is realizing how long the attack animation for each champion lasts. Once you attempt to cancel it and fail a few times (by cancelling the entire AA and consequently its damage), you'll pick it up quickly.