(If you want to double your effectiveness as a Catholic apologist in 30 minutes, read this article.)
Anthropology refers to the study of human nature in general, but within the context of theology it refers to man's nature as it corresponds to his final goal, his abilities, and the effects of Adam's sin. This subject is indispensable in forming good theology, especially when discussing salvation, because if you get this subject wrong, you'll likely get salvation wrong as well. As an analogy, if a medical doctor fails to understand how the body functions, he will most likely fail to properly diagnose and treat the ailment. Well-informed Catholic theologians have understood this and explained why incorrect anthropology is at the heart of the Protestant Reformation. Luther's decision to reject the One Holy Catholic and Apostolic Church came ultimately as a result of him severely erring on his view of human nature, and thus turning that into an erroneous view of salvation. From an apologetics point of view, any discussion with a Protestant is bound to fail if you don't understand that each side has issued a radically different "diagnosis" to the "illness" mankind finds himself in after Adam's disobedience.