When something is on the periphery of your vision, you can only see it when you’re looking sideways. Periphery means outside the boundary of something.
If you’re on the periphery of a group, you’re close to it but not part of it. A band on the periphery of a particular scene might have opened for another band a few times, but it's never headlined or gotten their big break. Periphery comes from a Greek word meaning "to carry around."