An agreement between countries to maintain a fixed exchange rate between their currencies. The Euro is a monetary union between 12 countries and the US Dollar is a monetary union between all States in the Union.
A monetary union involves two or more countries joining to create a joint currency that would be issued and administered by a common central bank. This is the model adopted in Europe with the creation of the Euro.
In economics, a monetary union is a situation where several countries have agreed to share a single currency among them, for example, the East Caribbean dollar. A monetary union differs from an economic and monetary union, where it is not just currency but also economic policy that is pooled or co-ordinated (as in the European Union Eurozone, for instance).