Elemental artifacts can be applied to a character's action skill (Mordecai's bird, Roland's deployable turret) in order to give the skill an elemental ability. They come in four types:
Incendiary
Shock
Corrosive
Explosive
When you receive your first elemental artifact, apply it to unlock the achievement and give your action skill an elemental ability.
Keep in mind, however, that you may be better off selling elemental artifacts after you find one you like, since they do not stack and you may only have one element active at a time. Applying additional artifacts simply overwrites your currently-applied element.