The problem of evil in its most basic form is: how can evil exist if god is omniscient (all-knowing), omnipotent (all-powerful) and omni-benevolent (good). Many people find fault in the way that god is portrayed in the Christian Bible because if god is supposed to be all-powerful, then why is it that he allows evil to exist? Why does he let bad things happen to good people?
The basic premise is that god cannot be all of these things and allow evil to exist. So the conclusion is that either god is not portrayed accurately in the Christian bible (ie he isn't all powerful, all knowing, and all good). Or as some people claim, he doesn't exist at all.