It may be a literal term referring to physical damage, though it is also used in colloquial conversation as a metaphor.
Overkill is especially used to refer to a destructive nuclear capacity exceeding the amount needed to destroy an enemy.
[1] The term is attested from 1946[2] and was in common use during the Cold War era, referring to the arms race between the United States and the Soviet Union.
Overkill colloquially refers either to use of force or weapons or to satiate the desire to humiliate a rival.
Overkill is a common feature implemented in many video games, typically representing the fact that the damage a single attack inflicted on an enemy or player character far exceeded the character's remaining health points.