This phrase emphasizes noticing something unexpectedly by using your side vision, without turning your head. While reading, I saw a flicker of movement out of the corner of my eye, and turned to see a bird fly by.
Pro Tip 2/3
Subtle Alert
It suggests an awareness of your surroundings that alerts you to changes, even while distracted. Lost in thought, I saw her leave the room out of the corner of my eye.
Pro Tip 3/3
Momentary Noticing
Indicates a brief, often unimportant observation that doesn't interrupt what you're mainly focused on. He didn't look up from his book, even when he saw a flash of lightning out of the corner of his eye.