In the political realm, an aspect of a candidate that will cost them votes no matter how they spin the situation. This is factually based on the Election of 1960 where John F. Kennedys's religion cost him votes. A woman running for president would have such a factor attached.
John F. Kennedy was a practicing Catholic and the first such Catholic running for president. Due to this fact of his religion, it cost him votes in the election. A number of Nixon votes were for the most part Anti-Kennedy, not Pro-Nixon. Since that time, such an unavoidable factor against a candidate was referred to as a Kennedy Factor.