Oxidation and reduction can also be explained using electrons. Oxidation is the loss of electrons and reduction is the gain of electrons. A helpful reminder is OIL RIG: oxidation is loss, reduction is gain.
When magnesium is added to copper sulfate solution, magnesium atoms lose two electrons each to form magnesium ions, so magnesium is oxidised: Mg → Mg2+ + 2e−. The copper ions gain those two electrons to become copper atoms, so copper ions are reduced: Cu2+ + 2e− → Cu. Equations like these, showing electrons lost or gained, are called half equations.
An oxidising agent takes electrons from another substance, so it is reduced. A reducing agent gives electrons to another substance, so it is oxidised. Here the copper ions are the oxidising agent and magnesium is the reducing agent. The electrons lost by one species are always gained by another, so oxidation and reduction happen together.