What is the Problem of Evil?

The problem of evil (PoE) is a philosophical argument. It is probably the strongest argument an atheist might have to justify atheism. It is said that the existence of evil proves that God is either not all good or not all powerful (and therefore does not exist as defined by monotheistic faiths). If God does not want evil to exist then he is not all that good. If he simply cannot stop evil then he is not all that powerful.