This is the name of the mistake: two people have been promised the same seat, room, or time. “There has been a double-booking” is what you hear at a desk when the clerk looks at the list and goes quiet. It is the same idea as the verb double-book; this form names the event, or the mess you are now in. It can also name the act in a general way: double-booking is how the error happened. You will meet it in hotels, planes, theatres, and appointment books. It is ordinary, slightly official service language. As with the verb, it is usually an accident — though actually a very full hotel on a holiday weekend may sound as if it happened on purpose. Still, in careful talk, a double-booking is “the same place given twice”, not “too many tickets sold on purpose” (that is overbooking).