To do something 'last minute' means something happened very recently. So in this sentence it means the hotel is booked right now (every room is occupied) BUT someone might cancel in the future. For example if someone has a reservation for a Tuesday, but cancels on a Monday this means it is a 'last minute' cancellation (as it happened very late)

One of the meanings of "to book" is "to reserve" (to schedule). I've booked one night at a downtown hotel. I've booked a table for two at a nice restaurant overlooking the ocean. I've booked an appointment with the dentist. I've booked a music lesson for Friday. "Cancellation" is the noun form of "to cancel." "We're fully booked but sometimes there are last-minute cancellations," probably refers to a hotel, but could refer to other situations. "We're fully booked but sometimes there are last-minute cancellations," is equivalent to "We (our hotel room, our restaurant tables) are fully booked but sometimes people cancel their bookings (reservations) at the last-minute." This statement is an indirect suggestion to the customer to call again just before the desired date. With luck, there will have been a cancellation and the customer can book the hotel room, restaurant table, ..., dentist appointment at the day and time that they want.