I'm going to assume you actually mean the phrase "in the long run", because "the long run" means just exactly that, a run which is long :)
"In the long run" means "over an extended period of time".
It is usually used to indicate that something which seems to be a certain way right now or in the near future, will most likely change to something else (better or worse) after a long period of time.
"In the long run physical beauty will almost always fade away"
