A gimp is the action of KOing a recovering opponent by interrupting their recovery, often with a rather weak attack that would not KO the opponent otherwise. Gimps tend to involve hitting an opponent off the stage followed by interrupting their recovery, capable of resulting in sometimes earlier KOs; simply interrupting a recovery that is otherwise sure to succeed can also be considered a gimp. Gimps put a large swing on a match, as they can happen at very low percentages, sometimes saving over a hundred points of damage needed to KO the opponent. Sometimes the term "gimp" is used to describe accidental SDs due to failed recoveries.
Gimping is related to and sometimes confused with edge guarding. Ganondorf hitting an opponent at 125% offstage with a sweetspotted up aerial and KOing them would not be considered a gimp, but just successful edge guarding. However, Ganondorf hitting that opponent at 50% with a reverse up aerial, semi-spiking them and causing their recovery to fail, would be considered a gimp. Edgeguarding involves continued and/or powerful hits that stop the opponent's recovery and possibly KO them; gimping is more "fluky", involving a relatively weak attack whose placement happens to net the KO for the attacker.
Common examples of gimps include:
A bonus somewhat related to gimping exists in Melee called Shameful Fall; it's granted by being at 50% or less and being KO'd by an opponent with 100% or more. The bonus penalises 1500 points.