If someone asks you to vacate the room, you'd better pack up your things and go. When you vacate something, you leave it behind, usually empty.
When you stay at a hotel, you're required to vacate the room at check-out time. The same goes for the last day of your lease on your apartment or after closing on the sale of your house. In all of these cases, you've got to get going and take all of your stuff with you. The verb vacate can also be used in conjunction with leaving a job, often an appointed office.