What does the idiom take down a peg mean?

This expression refers to a person who has an overly high opinion of himself (or herself) and probably should not be so arrogant. When such a person is "taken down a peg," it means someone else who is more knowledgeable or more skilled brings that person back down to where they ought to be. It does not carry a violent meaning-- the person who is brought down a peg is usually humiliated, because they are shown that they are not so smart after all, and they have to admit they were wrong and act more humble. (Another version of this expression is to "cut someone down to size.")