To run in order to escape something or to reach a destination quickly, perhaps before a certain time or before something happens. Our taxi was late picking us up, so we're going to have to make a run for the train when we get to the station! I couldn't wait to get out of school, and I made a run for the door as soon as the bell rang. Three inmates tried to make a run for it during outdoor exercise today, but they were stopped before they were able to jump the fence.