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. Higher affinities will allow the character to receive less damage from attacks of that element. An example would be the Fire Skull in Disgaea 2: Cursed Memories, having 50% in fire, -50% in Ice, and 0% in wind, so he takes less damage.
There is a fourth element, Star, but its damage is based straight off Intelligence and mitigated entirely by Resistance, having no modifier. However, in Disgaea 5: Alliance of Vengeance, the Star element is treated similarly to the fire, ice, and wind elements, meaning that it also has a affinity stat just like the other three, and thus are subject to the rules that the other elements have.
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 lots of damage with Fire spells and fire based attacks, but would do far less damage with wind attacks and even less damage with ice attacks. 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. Reincarnation can cause elemental affinities to change. For example, a reincarnated character that did great damage with Fire spells may change to have a Wind affinity instead, causing it to do miniscule damage with Fire spells and better damage with Wind spells, potentially resulting in the character having to learn wind spells to become effective with spells. Most storyline characters are exempt from elemental affinities, having 0% across the board, making them effectively neutral, and thus poor elemental spell users.
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 Aqua Demon 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.