When someone is suspicious of something, she can turn her head at said thing, and look at it through her peripheral vision. This conveys suspicion. Example: I was just walking down the dorm hall, and this girl I passed gave me the side eye. I guess she's suspicious of me, probably thinks I want to jump her.
THE SIDE EYE
Meaning of THE SIDE EYE in English
Slang English vocab. Английский сленговый словарь. 2012