Other forms: vacancies
Vacancy refers to something being unoccupied. If a hotel has vacancies, there are rooms available.
Have you ever noticed a store that's boarded up and empty, with signs like "For sale" or "For rent"? That's an example of vacancy: the store has no one in it. An unrented apartment is a vacancy, as is a house with no one living in it. Hotels put up a sign saying "No vacancies" when they have every room filled. It could help you remember what vacancy means if you know that a vacant lot is an empty lot.