The oxidation number of copper goes from +2 (in CuO) to 0 (in Cu), while hydrogen's oxidation number goes from 0 (in H2) to +1 (in water). The oxidation number of oxygen stays the same and is equal to -2.
In oxidation, the oxidation number increases as the species lose electron(s). Since the species gain one or more electrons in reduction, the oxidation number decreases.
Thus, hydrogen is oxidised while copper is reduced. We can also say hydrogen is the reducing agent, while the copper (II) oxide is the oxidising agent.