How much does it cost the airline if an aircraft misses its take-off slot?
A slot time is issued for aircraft flying through busy airspaces or to busy airports where the demand (number of flights) exceeds the capacity. If 50 flights are planned to arrive at an airport in 1 hour, but the airport can only handle 40 flights per hour, then the flow of traffic needs to be regulated.

Many years ago, everyone would simply depart, and then traffic would enter airborne holdings (circling in the air) along their route as they approached their destination, until there was room to land. Obviously, this is very inefficient, since planes would use a huge amount of fuel while waiting in the air.

Air traffic flow management was introduced to reduce this. Computer systems now calculate how many flights are planned to arrive at a certain airport in a certain time span. This calculation is done many hours in advance - so early, in fact, that the majority of the affected flights have not left their departure airport yet. This has the advantage that aircraft can wait on the ground, at their departure airport, soaking up the delay they will inevitable face. They will simply not be allowed to takeoff until a time where it can be assured that there is room for them when they reach their destination.

To achieve this, aircraft are issued a takeoff slot time (CTOT - Calculated TakeOff Time), at which time the flight must depart. If the flight misses this slot time, for one reason or the other, they are not allowed to depart - instead, they must request a new slot time. If flying to a very busy airport, the new slot time could be far in the future - sometimes several hours. This means that the plane must hold on the departure airport for several hours before being able to depart.

How these CTOT times are calculated is very complex, and deserves another question if you are interested.

While there are no direct costs from missing a slot time, getting delayed will cause many indirect costs for an airline - passenger compensation for delayed and missed flights, extra pay for crew (on the plane and at the airports) and so on. So the "thousands" it may cost an airline to miss a slot time come from these indirect costs of being delayed. Obviously, the exact amount will vary greatly from flight to flight.