A narthex is a room at the entrance to a church, separated from the nave with a low wall. It was common in early churches, and was used by cathecumens, penitents and others who were not allowed to be inside the church proper during Mass. They may be exterior or interior.
Few examples survive, but an interior narthex can be seen at Sant'Agnese fuori le Mura. With the development of the Gothic style, the narthex disappeared, and was replaced by a porch.
The term is often used about the interior vestibule or exterior porch, a usage which is strictly speaking incorrect, but very common.