Jumping is one of the basic movements of fighting games. It exists in almost all of them. It is often abbreviated with the letter “J” (e.g., “JA” or “j.A” would mean to hit the “A” button during a jump).
Characters in fighting games (like many games) can often jump much higher than one would expect someone to be able to in real life. In 2D games, at least, the general idea behind most jumps is to cut across an amount of space, including to the other side of the opponent (e.g., to escape a hit, or to use a jump attack in an attempt a crossup).
In nearly all fighting games, the jump input is thus:
In most fighting games, normal moves can be different even for the same button according to whether a jump is vertical or diagona. In Street Fighter II, there are also command moves that can only be performed during a vertical jump.
Some games (Guilty Gear, Melty Blood, Power Instinct, and Arcana Heart, to name but a few) allow one to jump again once (maybe even more) while already in the middle of a jump (“double jump”). This may be supplemented with the ability to rush forward in midair (“air dash”, in contrast with a dash on the ground). Other games will allow one to do another jump near the edge of the screen (“wall jump” or “triangle jump”).
More often than not, these special jumping abilities will be limited to certain characters in a given game.
Also, some games have different levels of jumps (generally due to the need for strategic jump speed and placement), such as KOF from ’96 onwards (which has normal jumps, big jumps, medium jumps, and small jumps), or Marvel (normal jump, super jump, “dash jump”).