To carry a process through from start to finish. Also one such carrying, considered as a single event.
Old English rinnan (to run, flow, move quickly), from Proto-Germanic *rinnan; a run is a process carried all the way through, the way a stream runs its channel to the end.
Carrying a process from its start through to its finish, or one such carrying counted as a single event — the same old word for a body moving and a stream flowing.