Screw with a looped head. Larger ones are sometimes called lag eye screws. Designed to be used as attachment point, particularly for something that is hung from it.
A vine eye (in the UK at least) is similar to a screw eye, except that it has a proportionally longer shank and smaller looped head. As the term suggests vine eyes are often used for attaching wire lines across the surface of buildings so that climbing plants can attach themselves.