What it means
Keep your eyes peeled means stay alert and watch carefully, usually when you're trying to spot something specific like a turning, a mate in a crowd, or trouble on the street. You're not literally peeling anything, it just paints a picture of your eyes wide open and scanning. Often said as a friendly warning on the move.
Usage examples
"Keep your eyes peeled for the exit, the GPS is lagging. If we miss it again, we're doing another ten miles and I'm buying coffee."
"Keep your eyes peeled for a parking space, anything legal will do at this point, I'm done circling."
"We kept our eyes peeled for the kingfisher all afternoon and saw it for about two glorious seconds."
"Keep your eyes peeled, yeah? Dave said he’s outside but that could mean anywhere within a three mile radius."
"Keep your eyes peeled for that little blue house on the left, if you hit the petrol station we’ve gone too far."
Where it comes from
This one’s been around in English since the 1800s. The image is literal and a bit daft in a memorable way: peel your eyes open wider so you don’t miss a thing. Nobody’s actually peeling anything, obviously. It stuck because it paints instant watchfulness in a way plain stay alert just doesn’t.