The meaning of "rocket" is the propelling engine - gasoline engines or jet engines - pushed by spouting hot gases.
Water Rocket use water and air to fly. The principle of Water Rocket propulsion is that, the compressed air spout water and the power of spouted water propel the rocket. Therefore the rocket that is filled only water cannot be propelled because the water cannot be compressed.
Likewise the following picture, fill the PET bottle with some water and pump the air into the bottle, then the air in the bottle will be compressed and the water molecules will be pressured, densified and trapped so it pressures both the inside of PET bottle and surface of water.
When the bottle cap opened water spouted out of bottle and it forces the PET bottle to fly. Due to it's great pressure the bottle propelled with great power. Obeying Newton's the third law of motion, "action and reaction" - every object has same reaction force against action - PET bottle propelled rapidly to the opposite direction of spouting water.
However one thing you have to be careful is that, without water or with lack of water, the air will leak, and the other hand with too much of water the bottle cannot fly far due to its heavy weight. 350 ∼ 400cc of water will be good for 1.5 L PET bottle for its maximum flight.