It's a colloquial way of saying someone left. But the general indication when you use "ran off" instead of "left" puts emphasis on some sort of avoidance. "I told him I love you and he ran off" pretty much means "he freaked out and avoided any further conversation." Whereas "I told him I love you and he left" usually leaves room for other things to have happened in between telling him and leaving, which the speaker did not specify. If you hear it the first way, there is no ambiguity. But if you hear the second phrase, you may still ask "well, what did he say?" because whatever did or didn't happen before "he left" is left unspecified. Also, if you use it as a verb, ie. "You totally ran him off" then you are saying you drove someone away- ie. they found whatever happened unlikable and exited the conversation/situation.

ran off = ran away = huir, escapar, evadirse, etc.