Defeating opponents can be overdone and is rewarded with some more spectacular death/defeat sequence than normal. Often results only in gibbing of the subjects, or turning them into explosions of gore, even when such makes no sense.
The first video game about Overkill was released in 1994.
Commonly involves characters exploding into gibs or otherwise dying in a manner that is way more than expected.
In terms of implementation, the simplest method likely involves going below certain level of negative health with the last attack or last attacks in the final 0.2 seconds or so.