When something happens inexorably, it keeps going and nobody can stop it. The word is rather formal — you meet it in news, history, and serious writing more than in chat. People use it for slow, heavy things: ice melting, an illness getting worse, a company going down, a deadline coming closer. There is a feeling of no mercy in it, as if you cannot talk the thing out of going on. Though actually, speakers sometimes use it just to mean “slowly but surely,” even when a person could still change course. That is a looser use. It is not a word for a small annoyance, like a late bus.