I tried to book a table, but the restaurant was fully booked.

book 在这里是动词，意思是"预订、预约"，通常用于预订座位、房间、票等。由名词 book（书）引申而来，因为过去常用账簿记录预订信息。 fully booked 是固定搭配，表示"全部订满、预约已满"的状态。