From this site, a good description of what this situation presents to one who has faith in God and in particular, the Christian God.
The so-called problem of evil is one of the most common objections raised against the Christian faith. Perhaps no one has more succinctly stated the apparent contradiction between an all-loving, all-powerful God and the existence of evil as the eighteenth-century Scottish skeptic David Hume:
"Is he willing to prevent evil, but not able? Then he is impotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Whence then is evil?"
More modern skeptics have sometimes posed the logical problem this way:
1. If God is all-good (omnibenevolent), He would prevent evil.
2. If God is all-powerful (omnipotent), He could prevent evil.
3. If God is all-knowing (omniscient), He knows how to prevent evil.
4. But evil exists.
5. Therefore, either God is not all-good, all-powerful, or all-knowing (or maybe He doesn’t exist!)
But why is the problem of evil a problem? In answering this question it is important to earnestly think through the following points, points which often are not reflected upon or not contemplated deeply enough. These considerations must be taken into account when addressing the problem of evil, especially from within the Christian worldview. When they are, I believe the problem of evil (POE) largely resolves itself.The site further breakdowns better different faiths addresses to the topic of evil:
How does each faith address evil:
Atheist: Regarding the origin of evil, it seems all the atheist can say is “Evil just is.” Nature is red in tooth and claw. No hope, meaning, morality, destiny.
Eastern Religions: For Hindus evil is maya, an illusion. Evil is not real. People suffer because of injustices performed in past lives (karmic debt). Therefore, suffering should not be alleviated since this would interfere with the karmic cycle and bring bad karma on the one attempting to aid the sufferer. This position prevents compassion and morally obligatory action in the face of horrendous evil.
Christianity: As Augustine argued, evil can be explained in part as the deprivation (or privation) of good. Evil is what ought not to be. Furthermore, since evil is not some “thing” but rather the privation of good, God is not the creator of evil. Rather, evil came as a result of free beings using their free will badly.
Answer to the Problem of Evil:
Apologists have shown the question can also be flipped on its head to prove God. Ironically enough, using that same question, the existence of evil can be turned into an argument for the existence of God.
1. If God does not exist, objective moral values do not exist.
2. Evil exists.
3. Therefore, objective moral values exist.
4. Therefore, God exists.
See more on this from Apologetic Junkie
A practical application from a site by apologist Ravi Zacharias:
“There cannot possibly be a God,” he said, “with all the evil and suffering that exists in the world!”
I asked, “When you say there is such a thing as evil, are you not assuming that there is such a thing as good?”
“Of course,” he retorted.
“But when you assume there is such a thing as good, are you not also assuming that there is such a thing as a moral law on the basis of which to distinguish between good and evil?”
“I suppose so,” came the hesitant and much softer reply.
“If, then, there is a moral law,” I said, “you must also posit a moral law giver. But that is who you are trying to disprove and not prove. If there is no transcendent moral law giver, there is no absolute moral law. If there is no moral law, there really is no good. If there is no good there is no evil. I am not sure what your question is!”
There was silence and then he said, “What, then, am I asking you?
The problem of evil stems from the contradiction we see in life and nature, precisely because we have a conscience (meaning con=with, science=knowledge) that informs us what is wrong with certain acts in this world. When we appeal to our conscience to try to disprove God through evil, we are in effect appealing to a moral law and trying to disprove the moral law giver. Without God, evil is just another way of expressing oneself right? After all who cares if everything is the product of chance, evil is natural then, no moral law could exist apart from something we make up to make us all get along better. If a moral law did evolve, why then is the enforcement of that law universal in nature?
The good news is that this evil will one day be abolished forever according to the doctrine of Christianity. Check out the claims of Christ. I suggest the Christian answer to evil is more in line with your conscience than any other world view. Trying to object to a moral law and disprove the law giver will not satisfy your conscience, dig deeper.