The hot air balloon rises when a fire is used to heat up the air inside the balloon.  When the fire is turned off the hot air escapes and the balloon drops back down towards the earth.  Why does the balloon take of when it contains hot air?

Think back, heat energy is similar to kinetic (movement) energy but on a much smaller scale.  Heat energy is often described in terms of the kinetic energy of gas particles, this is called kinetic theory.  Kinetic theory says that the hot gas particles inside the balloon will move more quickly than those outside because they will have more energy.  The speed of these particles is very important because at high speed they will strike the walls of the balloon with more force than the particles outside.  This results in a greater air pressure inside the balloon than outside.

This increase in pressure causes the balloon to expand just like when you blow up a party balloon, but when you blow up a party balloon you put in more air to increase the pressure which makes it heavier.  To inflate the hot air balloon you speed up the air particles to increase the air pressure which means less air is required.  This makes the balloon lighter so it floats upwards like a bubble floats to the surface of the water.