A ‘cancel’ is an action that immediately takes your character into the idle state. They’re particularly useful if you can use them to skip movelag, because then you get into the idle state much faster, making things safer and potentially allowing links that couldn’t otherwise happen.
Special GNT has three cancels:
This is a mechanic theoretically available to every character, although only a few can make good use of it. If, at any point, you connect with a melee attack while you are touching the ground and your opponent is not, you can press the Y button and spend 25% chakra to cancel the movelag and return to the idle state. In general, what matters is whether your character is grounded/your opponent is in the air at the end of the move, not the start. Honestly the easiest way to figure out whether a particular situation allows for y-cancels is to try them.
A couple of standard combos rely heavily on y-cancelling. Gaara uses y-cancels in the ‘gaara loop’ – B B A B A Yc _ ^A B A Yc… . Itachi can use y-cancels to combo into uncharged Amaterasu – vB A B B Yc vX
The Hyuuga cancel is a special mechanic for Hinata and Neji, where they can cancel the start of some moves into the idle state, for free. This is different to y-cancelling, which cancels the end of some moves into the idle state. In practice the Hyuuga cancel acts kind of like a free Y-cancel, because you can always continue a chain and then Hyuuga-cancel the next hit to skip movelag.
The Hyuuga cancel is performed by pressing Y during the startup of some moves on Neji and Hinata. Only some moves can be cancelled, and the exact cancel behaviours vary between Neji and Hinata, even for moves they have in common. Notable cancellabled attacks include the second attack in Neji’s B B chain, the second attack in Hinata’s B B chain, Neji’s >A (cancels after the dash forwards, so makes for an excellent way of quickly closing short distances), the second hit of Hinata’s >A A (also appears in some chains, allowing Hinata to quickly end chains), and Hinata’s >A when awakened (instantly, unlike Neji’s >A – this allows Hinata to perform an infinite).
Unlike the two cancels above, this is unambiguously a bug. It allows Minato to cancel the movelag of any move into the idle animation, as long as he is in desperation. It’s performed by entering <X whenever you want to cancel, and that’s it. Minato does have to be in desperation, though! This allows for a number of infinites – <B <X probably being the most amusing.
This works because in desperation Minato gets a kind of secondary escape-teleport special. You can enter vX to place a marked kunai, and then at any time you are in movelag or idle you can press <X to instantly teleport to the kunai. The implementation is a bit buggy, though – if there is no kunai to teleport to, Minato just instantly goes idle.