Resistances are used to determine how much damage reduction a unit gets from a certain element. Your character is affected by how much damage it can do against an enemy depending on how much resistance it has to that element. Your character itself also has resistances, and you are able to reduce elemental damage depending on how much resistance you have.
Note: Max resistance is 75%. Resistances may be shown by pressing the minimize button on table in the right hand corner of the screen.