It means to stand apart from the rest (in a good way), or to be the best. For example, "With his amazing grasp on the subject, John stood head and shoulders above the rest".
To be resistant to criticism. This is often said to young children upset over the fact that another child called them something that they did not like.
The tendency to keep (or steal) an object you touch. Also, to steal something quickly without anyone noticing. (ex: 'You stole that guy's wallet? You have some sticky fingers, my friend.')