The word premises refers to a house or other building, with all its grounds and any other buildings etc, belonging to it. The most typical phrase using this word is "on the premises", eg "The burglar has left the house, but I'm afraid he may still be on the premises" (he could be in the garden , the shed etc.) Of course you can also use the opposite: off the premises ("The police escorted him off the premises" would suggest that they took him out of the building, through the grounds and right off the property.)

When referring to property the word is always plural: "These premises are..." It comes from the medieval Latin word praemissa, which means "set in front."

The singular form, premise, is quite different: this can also be spelt premiss, and means a logical statement, on which another can be based.