What is meant by the term "theodicy"?

The question of theodicy is the question of how God's existence remains probable despite the problem of evil in the world. A certain theodicy is then an attempt to answer this question by giving a justification for God's inactivity regarding evil in the world. A theodicy must battle the difficulty of proving God's omniscience, all-lovingness and omnipotence despite the existence of evil. The book of Hiob in the Bible illustrates this dilemma. Can you think of why it is difficult to prove that God possesses all three properties? Try and imagine a scenario where God is all-loving and omnipotent, but not omniscient; one where he is all-loving and omniscient, but not omnipotent; and one where he is omniscient and omnipotent, but not all-loving. 

There are several approaches to an answer to this question. Most approaches follow the principle of the "free will defence": Precisely because God is all loving he has given us the choice whether to accept his word and act accordingly or not. The argument states that God could not be all-loving if he didn't give us a free will. The original argument was voiced by St Augustine who assumed the coming into existence of evil after a "human fall".
There are various versions of this argument, most of them hinge however as this theodicy only addresses the problem of moral evil and not the problem of natural evil. Do you have an idea why that might be the case? What is the difference between natural and moral evils?