'booked up' is an informal way of saying 'fully booked'. Examples: I'm sorry, I can't take any more clients that day; I'm booked up. I booked a room at a hotel. I tried to book a room at a better hotel, but they were booked up.

Just to add my voice to Bill's: Booked up means fully booked. You might be thinking of "booked in," which means that you've booked a hotel. They know you're coming and have reserved a room. Once the hotel is booked up, then they can't book anyone in any more.