Vacant means nobody is in it and nobody has claimed it. Think of the little sliding sign on an aeroplane toilet that flips between OCCUPIED and VACANT. A vacant seat on a train, a vacant flat with the curtains gone, a vacant lot where a building used to stand.
Jobs are vacant too: the vacant post of deputy head, advertised at the back of the paper. The noun is vacancy, which is the hotel sign reading NO VACANCIES and also the gap in the accounts team. The verb is vacate, which is what you do to a hotel room by eleven o'clock. There is a colder use for faces as well, since a vacant look or a vacant stare is one with no thought behind it. Vacant belongs to rooms, seats and posts rather than to people, so an empty bus is empty, not vacant.
1adjectiveemptyNot occupied or lived in, and available to be used or taken.
“The flat above the bakery had been vacant since spring.”
2adjectivevacantOf a job or position: not filled by anybody.
“Two seats on the council are vacant after the resignations.”
synonyms: open, unfilled
3adjectiveblankOf a face or expression: showing no thought or feeling.
“He gave the question a vacant look and went back to his soup.”
synonyms: blank, glazed
Also accepted in games: empty, unoccupied
Vacant reached English from Old French vacant, and Old French had it from Latin vacāns. Behind that lies a Proto-Indo-European root *h₁weh₂- for leaving a space empty, and it has kept English busy: vacuum, vacation, vacate and evacuate all sit on it. A vacancy is a hole in the world waiting for somebody to fill it.
Proto-Indo-European
*h₁weh₂-
Latin
vacāns
Old French
vacant
English, today
vacant
From Old French vacant, from Latin vacāns.
Etymology from Wiktionary, CC BY-SA