A leer is an unpleasant facial expression. A leer means the person doesn't like you, or even worse, does — in a creepy way.
Leer can also be used as a verb, meaning "to look at someone with a suggestive, rude, or contemptuous expression." Your sworn enemy might leer at you whenever you enter a room to express scorn and superiority. Leer derives from the Old English word hleor, meaning "the face or the cheek."