Getting Pure, or Getting Jewish?

Part of the conversion process—indeed, one of, if not the central parts—is immersion in a kosher mikveh. What did the rabbis of the Talmud intend by this requirement? Does it imply some sort of assumed impurity on the part of non-Jews? Or is it merely a ritual marker of transitioning between two identities? This class was given at the Global Day of Jewish Learning 2012.