A term to describe the situation where one of your Pokemon comes in after another is killed and kills the opponent in turn. Hence "revenge". You're basically sacrificing the first Pokemon to get one (or more) kills with the next Pokemon.
(Revenge killer is) A Pokemon whose main purpose on a team is to revenge kill or trap certain threats, usually those who your team lacks a solid defense against. Generally characterized by high Speed and frailty.
So, a revenge killer is a Pokémon which comes in after one of its teammates had fainted and revenge kills the opposing Pokémon. For example, if your Rayquaza-Mega fainted against Gengar-Mega, you send your Tyranitar to Pursuit trap it, thus "revenging" the Rayquaza-Mega kill. Mind that these Pokémon are usually either frail or fast, but sometimes they can be neither. A classic example is of Pursuit trappers, as Pokémon like Scizor-Mega, Tyranitar etc. sometimes are slow and bulky in some tiers.
Hope it helped.