Hydrogen peroxide (H2O2) is an oxidizer (or oxidizing agent). It reacts with the enzyme catalase (present in our blood), which catalyzes its breakdown and we end up with water, oxygen and heat (through this exothermic reaction). The relevant chemical reaction is given as:
`H_2O_2 -> H_2O + 1/2 O_2`
This is the reason why application of hydrogen peroxide on cuts causes stinging and foaming. When hydrogen peroxide is mixed with blood (in experiments), we can see that we will end up with more water than what we started off with (in terms of concentration) and also more oxygen than the beginning of reaction.
George Senter is credited with the discovery of some catalyst (which we now know as catalase) that enables the decomposition of hydrogen peroxide with blood.
Hope this helps.