Attack cancels are a technique in Super Smash Bros. Clash. This is basically the catch-all term for canceling the animation of a normal attack into a special attack or other attack. While the mechanic is new to Super Smash Bros. Clash, this has been a key mechanic to combos from the start of other fighting games.
Attack cancels are mostly used in combos, or to cancel an unsafe attack into something that provides you with some shielding. Attack cancels are actually quite difficult to connect with unless canceled right as a normal attack hits due to the short hitlag most attacks have in the game and Smash's knockback system, and the ones with long hitlag usually have massive knockback or damage regardless.
Some characters, such as Ryu have a bit more hitlag on their attacks than other characters, making basic cancel combos easier. For example, Ryu's Down Strong into Hadoken cancel combo is pretty easy to perform. Attack cancels can also be done anytime in a normal attack meaning you can cancel multi-hit attacks during the frames prior to the last hit into specials easily.
All normals (except some Smash Attacks) and most specials (most reflectors can't be) can also be canceled into Clash Attacks with the same rules as normal into special cancels. Some special moves provide a lot of hitlag though, so this is generally a bit easier.
Regarding Final Smashes, in order to keep the game balanced characters cannot cancel directly into Final Smashes for the most part. All taunts that are capable of hitting an opponent can be canceled into Final Smashes, as well as some other attacks such as The Dog's Great Laughter.