To enlighten someone means to explain something clearly to him. If your friend is behaving strangely but insists she has a reason for it, you could ask her to enlighten you.
Enlighten comes from the metaphor that ignorance is a state of being "in the dark," and that knowledge is illuminating. We use enlighten as a verb meaning to clear up, to remove confusion. Light is also a powerful metaphor for spiritual insight. If you have a great revelation about the divinity of the world, you could say you have been enlightened. The era known as the "Age of Reason" is also called the Enlightenment.