A person of great or fine repute is someone who's widely known and highly respected. The word has a stuffy feel, so you're better off describing a cellist as being of great repute than, say, a rapper or comedian.
Like the words reputation and putative, repute comes from the Latin word putare, which means "consider." And the re? Let's say that the cellist Yo-Yo Ma is widely respected. That means a lot of people consider him to be great. He's considered great not just once but again (and again and again).