To finish something is to complete it or bring it to a conclusion. If you finished a race, you completed it — even if you didn’t come in first.
Finishing is about concluding. If you finished a novel, you read the whole thing. Finishing a job means the job is done. This word can also refer to a coating or polish used to make furniture look nicer or fancier. If you say someone has a finished look about them, they don’t actually have a coating or polish, of course — but the effect is the same. They have a clean, cultured, polished appearance.