Density is the measure of mass present per unit volume. Lesser the density, lighter will be the object. Now, density varies with temperature.
When a hot air balloon is on ground, the air inside and outside the balloon is of same temperature and density. However, when we turn on the burner of the balloon, the air inside the balloon starts getting hot. The molecules of air move faster and spread apart, taking up more space.
Hence, the air inside the balloon becomes less dense than the air outside. As less dense air is lighter, the hot air balloon rises and thus, begins to float.