Originated in Quake II and made popular in Unreal Tournament.
1) A players health is such that upon being killed in a multiplayer game they explode into many gibs and giblets (peices of simulated flesh and gore). (Quake 1)
2) A game mode where every weapon (usually only a hitscan railgun/ASMD) instantly kills the player in one shot. (Started in Quake 2 and popularised as a mutator in Unreal Tournament)
3) Finding yourself at the bottom of a chasm/lava/force field and being instantly turned into gibs when you touch the bottom.
So I was running around and a spammed a rocket into a door and it slapped this poor sucker in the face. I then jumped off the top of the level and instagibbed him with my railgun as I was falling. Dont think he had time to blink!
Battlefield: That guy killed me as soon as I turned the corner.
Defense Of The Ancients: Care man, they will instagib you if you go too far alone.