The School of Illusion involves manipulating the mind of the enemy. This skill makes it easier to cast spells like Fear, Calm, and Invisibility.
Stealth-Mage tip: If your character build is geared towards a stealth character that uses conjured weapons, such as Bound Bow, or Bound Swords, getting the Quiet Casting perk is invaluable. Here is the easiest way for a non-illusion character to obtain Quiet Casting:
Once you learn the spell, proceed to continuously cast it to start grinding Illusion skill levels. By the time you get to Illusion skill-level around the upper 50's, you'll have gained enough perks to be able to invest and purchase Quiet Casting. (You can also use the perks on other skills, if you have no need for stealth casting)