An oxidising agent is one which oxidises(oxidation number increases) others and itself gets reduced. Whereas a reducing agent reduces (oxidation number decreases) others and itself gets oxidised.

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.

So, we can see that H₂O₂ acts as an oxidising agent in the first reaction as it increases the oxidation number of I^- in HI from -1 to 0 in I_2.

Similarly, H₂O₂ acts as a reducing agent in the second reaction as it decreases the oxidation number of Cl⁺ in HOCl from +1 to -1 in Cl^-.