A Kara cancel is the canceling the startup of a move into another move. This name comes from the Japanese word 空 (kara), which means empty or sky. You are canceling the startup of the first move such that it never comes out (and thus empty).
At this point you may wonder why can you cancel the startup of a move? Developers put this into the game to act as a way to make special attack inputs a bit more lenient. For example, a player mistiming a Template:236 as Template:236~. Competitive players have found more advanced applications for this.