When you do something on time, you do it right when you should — you're not too late. It's important to show up on time for a train, or it may leave without you.
If you're always on time, you're punctual: you can be depended on to arrive when you say you will. If you pay your bills on time, you'll never get a late notice or fee. People who are never on time, however, are always late. The adverb phrase on time was first used in the late 1800s.