Skills help rate your characters' proficiency in certain tasks. Most spells and abilities have an associated skill. By using skill points, you can become better at that spell or ability. Skills are also used to demonstrate proficiency with weapons and armor. Increasing those skills allow a character to become better with that weapon (increased damage and accuracy) or armor (increased protection).
You can find your character's skills by pressing the C key - to go to the character menu, then jobs, then skills.