A statement that "proves" itself to be true, with itself as the only evidence. For example, "Everything I say is true."
A circular argument based on that statement would be to say that the statement is true because I made it, and everything I say is true.
Some people believe the Bible to use circular logic, since it is said to be the word of God, and it says that God exists. This equates to saying that "God exists because that book says so, and that book was written by God".