Many reactions can be described as oxidation or reduction. In terms of oxygen, oxidation is the gain of oxygen. When magnesium burns, 2Mg + O2 → 2MgO, the magnesium gains oxygen to form magnesium oxide, so magnesium is oxidised.
Reduction is the loss of oxygen. When copper oxide is heated in hydrogen, CuO + H2 → Cu + H2O, the copper oxide loses oxygen and is reduced to copper. At the same time the hydrogen gains oxygen to form water, so hydrogen is oxidised. Oxidation and reduction always happen together in the same reaction.
An oxidising agent gives oxygen to another substance, so the oxidising agent is itself reduced. A reducing agent takes oxygen away from another substance, so the reducing agent is itself oxidised. In the copper oxide reaction, copper oxide is the oxidising agent and hydrogen is the reducing agent. In the same way, in Fe2O3 + 3CO → 2Fe + 3CO2 the iron oxide is reduced and the carbon monoxide, which is the reducing agent, is oxidised.