A goof is a silly fool. If you can't stop telling jokes, even after your math class has started, your teacher will think you're a goof.
There are many alternate words for goof, including dimwit, dummy, and nitwit. In other words, you should only call someone a goof if you mean to insult their intelligence. The mistakes a goof — or anyone — makes can also be called goofs: "I made such a goof when I was mixing this cake batter." Goof is a 1916 American invention, probably influenced by the English dialect goff, "foolish clown."