Great question, one that bothers a lot of people. Frankly, there's no easy answer. But there is an approach we've found helpful in trying to at least partially understand why God allows suffering and evil in the world.

First of all, we need to understand that it is people, not God, who cause most of the evil and suffering in the world. C.S. Lewis once said that four-fifths of the evil in the world is done by humans to other humans. Humans kill, torture, rape, force children into slavery, etc. Humans do this because the human race is sinful and in rebellion to God.