Airline booking is similar to other booking systems like Bus Booking. In the most simplest terms we can understand it as that we have limited number of seats and we need to book that to the person for particular day and time. Also, when it gets booked, we need to remove it from available seats and which does not allow other person to book the same seat.
So for a start, in this system we need a database table to store booking info for each seat. So, to check whether any particular seat is available or not. The system will search the seat number booking info in that table, and allow another booking only if it does not find reservation for that particular time slot.