The three Elemental Affinities of Fire, Ice, and Wind dictate how a unit responds to one of the three viable elements. Having higher percentages means the element is favorable, while lower percentages means it is not. An example would be the Fire Skull in Disgaea 2: Cursed Memories, having 50% in fire, -50% in Ice, and 0% in wind. There is a fourth element, Star, but its damage is based straight off Intelligence and mitigated entirely by Resistance, having no modifier.
Aside from mitigating elemental damage taken, the elemental affinity also affects the powers of magical spells. As stated with the Fire Skull, he would do well with fire based attacks, be neutral in wind, but would take extra damage from ice. Weapon/monster skills aren't boosted with affinity. Only defender's affinity matters for Weapon/monster skills.
Most created units start with 0% in one stat, 50% in another, and -50% to balance it out. Most storyline characters are exempt, having 0% across the board, making them effectively neutral.
In Disgaea 2, three units had elemental protection, meaning that one particular element had no effect on them. Under certain circumstances, these units could even absorb the element. The Dragon was associated with Fire, the Warslug was associated with Ice, and the Caith was associated with Wind. A fourth unit, Holy Dragon, has protection from attacks that do not carry an elemental attribute.