A jump-canceled grab (or JC'd grab) is a technique in Super Smash Bros. Melee where a character interrupts a dash or run with a jump, which itself is then jump-canceled with a grab during the jumpsquat animation. This results in the character using their standing grab while maintaining some momentum from their dash, the amount of which is based on their current speed and traction.
Jump-canceled grabs are used for two main reasons. Firstly, essentially all characters' dash grabs are much slower and laggier in comparison to their standing grabs; being able to use them while still keeping some forward movement therefore results in a much faster and safer grab. Secondly, the forward movement effectively increases the range of the grab compared to a stationary grab, making them easier to keep opponents in chaingrabs with throws of forward trajectory (such as Captain Falcon's down throw) or involving enemy DI (such as Mr. Game & Watch's up throw).
This technique is not possible in other games, as grabs cannot be used out of a jumpsquat in them. However, dash grabs in Super Smash Bros. Brawl and Super Smash Bros. 4 are generally faster and more reliable than in Melee, while the original Super Smash Bros. allows characters to use their regular grab out of a dash nevertheless, due to the lack of dash grabs in said game. In Brawl, experimentation shows that, if jump-canceled grabs were to exist in said game, the amount of character momentum given would be significantly greater than in Melee, especially for fast characters with low traction such as Captain Falcon.