A leer is a grin that isn't friendly. 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 or rude expression." Dirty old men might leer at every girl who walks by, but another reason to leer is to show scorn, like a dirty look your enemy gives whenever you enter the room. Just hope this person outgrows the habit of leering — it's a very immature and off-putting gesture.
