Originally stemming from fear of Communism (ie the red-scare),it means you were suspected of being involved in Communism, and were put on a list with other such people, though most had done nothing wrong. Being on this list prevented you from doing lots of everyday things.
More recently associated with
Seinfeld, when
Elaine got herself, and then her boyfriend, blacklisted at the best delivery
Chinese Food place around. They refused to deliver to the people "on their list."
(note: I have not seen this episode for many years, so forgive me if this is not verbatim, but it is pretty close)
Delivery Man: here's your food
Elaine's boyfriend: thank you
Delivery Man, seeing Elaine: I know you! You're on our list!
Delivery Man, to Elaine's boyfriend: Now YOU are on our list, too!
Elaine's boyfriend, to Elaine: You got me blacklisted at
Hop Sing's!?!?