The phrase "running late" refers to being behind schedule or not arriving at a planned time. It often implies that someone had set a specific time to be somewhere but is delayed in getting there, which can happen due to various reasons such as traffic, late departures, or unexpected events.
The phrase "running late" combines the verb "run," which in this context means to progress or make one's way, with the adjective "late," deriving from the Old English "late," meaning delayed or occurring after the expected time.