Jump Cancel is a technique that appears in every Devil May Cry game. It allows the player to interrupt virtually any of the protagonists' techniques by leaping off the enemy at the exact frame in which they touch their foes, usually by using the Enemy Step or Leap abilities.
Attacks like Rebellion's Aerial Rave that keep the enemy close widen the window of opportunity for leaping off of enemies, while attacks like Yamato's Slash Dimension C that push the enemy away make it much more difficult to achieve accurate timing. Certain attacks cannot be efficiently jump canceled at all; for example, the damage from Arbiter's Drop is generated by the shockwave, rather than the axehead hitting the enemy, so attempting to jump cancel would result in a whiffed attack.
In Devil May Cry 4, Nero can use his Snatch technique in conjunction with Jump Canceling to climb indefinitely, while in DmC: Devil May Cry, Dante can use the Ophion's Demon Pull and Angel Lift in conjunction with Jump Canceling to achieve the same result, although his Devil Trigger can also be used to make this process easier and widen the window of opportunity. This process is actually required within normal gameplay to acquire a Gold Key in Mission 9.