By heating the air inside the balloon with the burner, it becomes lighter than the cooler air on the outside.
This causes the balloon to float upwards.
Now if the air is allowed to cool, the balloon begins to slowly come down.
This image here is depicting how the warm air lifts the balloon and cold air from the surrounding rushes to fill the space created by warm air which inturn supports the upward movement of balloon.
Pilots have a great deal of control over the altitude of the balloon, which they monitor with various instruments.