1. A person who acts silly or foolish. (One who acts goofy; see also goofball).
2. A mistake, often a small or silly one. (To goof up).
3. To goof off is to waste time, or to take it easy. Also goof around, goof about.
4. To goof on someone is to ridicule and make fun of them.
All of these are used in American English, although are probably used more by children than adults. They also have a 1950s feel to them. You don't hear them as much these days, although they are certainly still around.
Goof was first recorded in 1906, originating in America, and meaning a stupid person. It may come from the word 'goff', used in some English dialects to mean a foolish person or a clown. Etymonline.com reports that it's usage in the sense #2 (above) is from 1954 (although 'goof up' is from 1941), and #3 is from 1932. Both are proceeded by 'goofy', appearing in 1921.
And one more:
5. Prison slang for a child molester, particularly one who went after young boys. One of the worst insults in prison, it's probably not a good thing to call anyone who has spent any time on the inside.