A theodicy is theistic attempt to explain why evil exists in the world dispite the existance of God. Knowledge of theodistic arguments can help an atheist counter these arguments.
Theodicy is not found in all theistic beliefs, but is common to the three primary monotheistic religions (the Abrahamic traditions) of the western world.
The need for theodicy is based on a specific set of assumptions about the nature of god and the world. In religions which do not formulate god(s) in the following mannor, theodicy will not be present;
1. God is omnibenevolent (God is completely good.) 2. God is omnissiant (God is all-knowing.) 3. God is omnipotent (God is all-powerful.) 4. Evil exists in the world. (Not generally up for debate.)
Do not assume these are the beliefs of all theists. Polytheism, for instance, would specifically disagree with point 3, and usually disagrees with points 1 and 2. Some polytheists may even point to theodicy as a reason to prefer polytheism over monotheism.
Two Common Theodicies
St. Augustine's Theodicy: Blame it on the Fall from Eden -explication needed-
St. Irenaeus's Theodicy: Evil serves a purpose. It will make us good people. -explication needed-