They're a bunch of hate-filled individuals that call themselves the "Westboro Baptist Church." See Wikipedia for a description: http://en.wikipedia.org/wiki/Westboro_Baptist_Church. They're definitely not Catholics, and I don't think they're really considered Baptists either. I'm not too familiar with all the branches of Christianity, but they say they are a denomination of it even though others seem to disagree with them.
Anyway, "fighting words" are a legal classification of words that can be reasonably expected to cause violence. They reason they're important is because they're not protected by the First Amendment of the Constitution and can therefore be punished.