In the notes on redox, we mention that hydrogen peroxide can be oxidized or reduced, depending on what other chemical is added to it.
When hydrogen peroxide is oxidized, it is converted to oxygen.
When hydrogen peroxide is reduced, it is converted to water.
Hydrogen peroxide can also undergo disproportionation, which means it is oxidized and reduced simultaneously. Water and oxygen is formed when this reaction takes place, as illustrated in the equations below:
hydrogen peroxide --> water + oxygen
2H2O2 ---> 2H2O + O2
The following is a cute video showing the disproportionation of hydrogen peroxide: