What happens to air when it heats up

The molecules in the air begin to move faster and further apart from each other. There is still the same amount of molecules in the air, it has just expanded as it heats up.

Warm air takes up more space than the same amount of cold air, it also weighs less than cold air occupying the same space.

For example, a hot air balloon. Without the heated air, it would't be able to float.