What is political party affiliation?

The political party or organization to which you belong or with which you are registered.

In most U.S. states as well as other countries, a person who registers to vote is asked to declare a choice of political party. Thus, there are "registered" Democrats, Republicans, Libertarians, etc., and that is the affiliation. It once was common to issue membership cards to supporters of political parties or organizations. Thus, the term "card-carrying member" of a given party or group.