The "eye" of a potato is a small sprout or bud that grows on the potato. Each tuber has many notches or axillary buds or small sprouts called eyes, and from these buds, a new potato plant can grow in favorable conditions. The eye of the potato is the growing point on the potato tuber, and it contains a little stem bud. While the sprouts themselves are not safe for human consumption, you may be able to save a potato that only has a sprout or two. Use a paring knife to remove the entire sprout. A peeler will only get the surface, so make sure to use a knife to really exorcize the sprout from the potato.