In the gas phase, hydrogen and oxygen take up an incredibly large volume, so they are condensed into a liquid to fit into a smaller, lighter tank; this is a physical change. To condense these gasses, we must cool them to extreme low temperatures:
Oxygen is a liquid between 45-90 K,
Hydrogen is a liquid between 14-20 K.
Like any combustion, this reaction produces energy, firing out the produced water at high velocity to thrust the rocket upwards. It always rains after a rocket launch because the water ejected from the rocket condenses into rain.
Figure 1 - The combustion reaction for hydrogen