Interruptibility is the ability to begin a new action even though the current action's animation has not yet finished. For example, while Mario's forward smash in Super Smash Bros. Brawl takes 56 frames to complete execution, the player can interrupt the ending frames and do something else as early as frame 48. For most intents and purposes, this results in the last part of the animation simply being filler, as the player is likely to attack, jump, or simply move as soon as possible. Many attacks have a minor amount of interruptible frames during their ending lag, while in general special moves and get-up animations do not; some attacks such as Marth's or Ness's down tilts have a significant interruptibility window which allows them to follow up the attack much faster than the animation would suggest.
In Super Smash Bros., interruptibility is not very common, only being used at the ends of some taunts and non-final neutral attacks. Super Smash Bros. Melee expanded interruptibility's applications to many attacks, and Brawl continued the idea as a common mechanic.
It is possible for actions to be interruptible with only certain kinds of actions, such as the case with jump cancelling.