To answer the question of why evil exists in our world, we must first define evil. Webster’s defines it as: “morally wrong, harmful, injurious, misfortune, and suffering”. This definition has two aspects: a moral component and a suffering component.
If we are talking about the suffering aspect, we must ask if all suffering is evil. It is not from our own experiences. Good parents do not inflict evil on their children but they do allow their children to suffer pain. One example is a medical procedure that is painful but beneficial to the child in the long run. A second example is parents allowing a child to fail at a task to teach the child independence and that effort is required in life but that effort alone does not guarantee success. A third example is parents allowing a child to play and in playing that child hurts himself. Do we consider the parent responsible for all this suffering? No. Children will suffer because of the characteristics of the material world in which we live and because parents cannot control every action of their children. So when we adults suffer, why do we blame God?
So we must redefine evil as causing or allowing pain, trouble, suffering, or misfortune with no purpose of the betterment of the individual affected. This is the moral component in the definition of evil. However this definition is still insufficient. If it were sufficient, the Inquisition would not be considered evil because the perpetrators of this human event had only the future good of the individuals they tortured and killed in mind: the eternal salvation of their soul. What we are still lacking in our definition of evil is free will. Evil causes suffering with no purpose of the betterment of the individual and with no view of that individual as a unique creation of God with the right to make their own decisions.
We have learned that our material world, Satan, and we humans all produce the evil and suffering in this world. The only way God is responsible is that he allows the continued existence of this material world, of Satan, and of us humans. However, God does have a purpose of bettering our lives and, just like parents, God allows us to suffer because it is the best way to teach free agents how to live their lives. Personal experience touches our soul in a way that other types of knowledge cannot. If we make our own choices, we will make mistakes and those mistakes will cause suffering. If we cannot make our own choices, we will never learn.
While at times our suffering might seem severe and unnecessary, Huston Smith sees it from a different perspective:
If a two-year old drops her ice-cream cone, that tragedy is the end of the world for her. Her mother knows that this is not the case. Can there be an understanding of life so staggering in its immensity that, in comparison to it, even gulags and the Holocaust seem like dropped ice-cream cones? 
Lance Armstrong asserts that his struggle with cancer made him a better person and that it takes a crisis for us humans to realize our full potential.
What if I relapsed and the cancer came back? I still believe I would have gained something in the struggle, because in what time I had left, I would have been a more complete, compassionate, and intelligent man, and therefore more alive. The one thing the illness has convinced me of beyond all doubt—more than any experience I’ve had as an athlete—is that we are much better than we know. We have unrealized capacities that sometimes only emerge in crisis. 
Christianity teaches that God has a purpose that transcends all the suffering that occurs. God allows evil and suffering to exist in our world because he respects our free will. He allows us to make mistakes and learn the consequences of those mistakes. He used the mistakes others make to provide more opportunities for us to learn. He uses the actions of Satan and the sometimes destructive nature of our material world to teach us lessons about ourselves like he taught Job.
We humans desire a life of ease but if we are to learn, if we are to grow, if we are to learn of our true capabilities, then we must face difficult times.
 Huston Smith, Why Religion Matters (San Francisco: HarperCollins, 2001), p. 254.
 Lance Armstrong, It’s Not about the Bike (New York: Berkley Books, 2001), p. 267.