"know of" means you know they exist. "know" means you know them personally. Sometimes they can be the same, sometimes not. You could say "know of" if you have heard of that person, or have heard of their reputation, but have never actually met them.

They are very similar and the general rule is "know somebody" means you know the person well and "know of somebody" means you know who they are. You know a friend but you know of a celebrity.