the swinging leaf of a door or gate, the panel that opens and shuts
This word names the moving leaf itself, the wooden or bronze panel hung on a pivot that you push open and pull shut. It is not the doorway or the gateway, which are the framed openings; it is the slab that fills the opening and turns to close it. A house or city gate was often closed by two leaves meeting in the middle, so the word frequently appears in a paired form meaning a set of double doors, regularly mentioned together with the bar that holds them locked.
From that one solid image the word stretches in natural ways. A city's gate-leaves stand for its defenses, so to break or open them is to conquer or to surrender the place. Poets speak of the doors of the sea, the doors of the womb, the doors of heaven, and the doors of a creature's jaws, picturing a barrier that God or nature can hold shut or swing open. And because a leaf is a flat panel, the columns of writing on an unrolled scroll could be called its doors, as when a king slices off the panels of a scroll one section at a time.
All of these are the same object seen in different settings: a flat panel that closes an opening and can be opened again. The senses below sort the occurrences by what the leaf belongs to, but the core picture never changes.