Physical, Magical and Mental resistances are used to determine the chance to avoid an attack that targets those defences.
For example, a magic attack that targets your Magic resistance will need to beat your score in order to land. Each power usually clarifies which defence they target in their description.
In terms of damage reduction, the other resistances are more useful. All elemental resistances (penetration, fire, blight, storm etc...) give their damage reduction as a percentage. They won't prevent you from being hit, but they will reduce the damage of the attack.