Execute is a rank 5 skill from Sword tree. It allows a character to instantly kill any target, regardless of its health, armor or resistances. To use it, a character must target the skill on an opponent, and do any damage to its health on the same turn. Two ways to do it currently are using the Trow Rock ability (a free action), or to Inspire the character to let them make an attack move again. If this second attack does damage, then the target dies immediately, regardless of damage received. If the second attack misses or is deflected by a shield, Execute will not activate.
Note: the target dies even in non-lethal mode, so do not Execute those you want to keep alive.