Jump checking is the art of not allowing the opponent to jump. Alternatively, smashing an incoming jump.
This has a slightly different meaning from anti-air, however; while anti-air is generally intended to take on an opponent who has already taken to the air, jump checking is generally intended to keep an opponent from getting a good jump by smashing its outset; it is used when they are getting off the ground, before they can do it, or if they look like they are going to.
Anti-air is usually accomplished with special moves and super special moves, whereas jump checking requires speed and proximity, meaning that it is generally done with normal moves that have a high strike height. Good examples include the standing A’s in Melty Blood (for practically every character) and Ralf Jones’ far standing C.
Like noted above, unlike anti-air, jump checking uses simple normal moves, but since these practically never have invincible hitboxes, a mistake can get you stuffed, and you will likely take lots of damage because of it. Therefore, you must use it carefully, with tactics.