Which exercise has a person lying face down and lifting the chest by extending the spine? The exercise is a back extension.
A back extension strengthens the muscles that extend and stabilize the spine, especially the erector spinae group. In a floor version, the person lies prone and lifts the chest, sometimes raising the arms or legs as well. On a Roman chair or back-extension bench, the hips or thighs are supported while the torso moves from a bent position toward alignment with the legs.
The term hyperextension is often used for the same gym exercise, but it can be misleading. In ordinary exercise terminology, it usually means extending the spine from a flexed position; it does not necessarily mean forcing the joints beyond their normal range. Controlled movement and a neutral neck are important because excessive arching can place unnecessary stress on the lower back.
Back extensions are sometimes confused with reverse hypers. A standard back extension primarily lifts the torso, while a reverse-hyperextension machine fixes the upper body and swings the legs. Both can train the posterior chain, but their movement emphasis differs.