1. I’m looking for a special edition of a book, and I haven’t found it anywhere. When you’re in the bookstore, please keep your eyes peeled for it, will you?
2. They planned to meet Joe on a crowded corner at lunchtime. He hadn’t arrived yet, but as people walked toward the corner, they kept their eyes peeled for him.

The expression suggests that one’s eyelids are pulled back in order to not miss seeing anything.