The problem of evil
Cf. Catechism, paras 385, 395, 400, 412
If God is good, and omnipotent, why does he allow evil, such as the suffering of the innocent? Traditionally, there are several types of answer to this question.
One of them says that our world is the best possible: no good world can be created that does not operate according to regular rules and laws of nature. Suffering may be a necessary punishment, or it may be a random fact without intrinsic meaning - but either way the evil is always more limited than the greater good that it may serve in the Providence of God.
If that seems callous, the Augustinian tradition explains the mystery of evil by appeal to another mystery: the mystery of freedom. All evil, all sadness, all cruelty and ultimately all misfortune, if it does not come directly as a lesson to restore wisdom or a punishment to restore justice (and even then), originates in the misuse of free will - a choice against Godís own will, which God permits to happen, once again, for the sake of a greater good, namely the existence of freedom itself, which includes a freedom to reject God. This freedom is an essential part of our dignity as human beings.
We live in a fallen state, a fallen world, conditioned by a choice that was made by the Angels and by Man in the beginning of things. In that choice, all creatures have to some extent been caught up: we call it Original Sin, and it includes a predisposition towards further personal sin, a weakness of the will that can only be rectified by Grace. It may also explain the fact that nature as we experience it is "red in tooth and claw".