The oxidising state of the oxygen atom on H₂O₂ is -1 which is an intermediate state. It means that it can either reduce itself to H₂O where oxidation state of O is -2 or it can oxidise itself to O₂, where the oxidation state of O is 0.

In the first case, H₂O₂ acts as an oxidising agent and in the second case, it acts as a reducing agent.