These terms refer to the strength of the fragrance. Parfum (generally the most concentrated form you can buy) has 15-25% perfume oil dissolved in alcohol. Any mixture with a lower proportion of oil to alcohol is an eau (water).
Eau de Toilette: 4 - 10% perfume oil
Eau de Parfum: 8 - 15% perfume oil
Parfum: 15 - 25% (Also sometimes referred to as extract or extrait)