1. To wander on(to something or some place), especially when one is not supposed to be there. I keep an electrified fence around my fields to keep wild animals from straying on at night. Be sure not to stray on Old Man Cratchit's land—he's liable to shoot you if he catches you!
2. To wander around on some area or piece of land. We spent the afternoon straying idly on the beach. I watched the kids straying on the field across the street, trying to catch the falling snow on their tongues.