The premises of a property consist of the land and buildings on it, usually of a business or organization. If there are no dogs allowed on the premises of a school, you'll have to leave your furry friend at home.
A game of hide-and-go-seek where you can’t leave the house will go a lot faster than one that permits hiding anywhere on the premises, including outdoors. Premises has another, unrelated meaning — it can also be the assumption or hypothesis from which a conclusion is drawn. The English writer Samuel Butler said, “Life is the art of drawing sufficient conclusions from insufficient premises.” Meaning, much of life is about guesswork.