The principles of water rockets are very similar to that of actual rockets. Real rockets use gas or other vapors for launching, but water rockets use water. However, the 'action-reaction' law for gas, vapors, and water are all the same.
Water in water rockets takes on the role of fuel, and by consistently releasing it; air becomes pressurized and changes into energy. Because the density of air is low, it is easy to pressurize and therefore much air fuel can be stored inside of a PET bottle.
When it leaves the bottle, the air expands very rapidly, thus disallowing the water rocket from flying far.
On the other hand, liquid such as water has the advantage that it discharges in one direction, however it is hard to pressurize. Using the characteristics of both air and water, the liquid which is non-pressured is given high pressure by vapors. This is then rapidly released to create thrust force, while simultaneously the rocket receives motion energy relative to the energy discharged in the opposite direction.