My best assumption on the term origin is how it works: The moment the actual "firing function" is executed, a path from the muzzle to infinity is drawn, and scanned for intersections with a hit-box or a collidable object. Or in the really old days, the pixel you aim at was scanned if it cointains a hit-able object.
(Which is not necessarily the same as the moment the player pulls the trigger or the weapons starts executing the firing sequence or the animation is displayed.)