Used in public as a replacement for asshole, but usually in reference to someone who is such an asshole that they will not even realize that you are talking about them.
Anyone so hateful, chauvinistic, bigoted, etc. that they should wear their ass for a hat. Usually, but not always used in reference to someone who is willfully ignorant, hypocritical, and/or has extreme homophobia, religious intolerance, or fascist ideology.
See also "Fundie"
The leader of that country just justified invading their neighbor country as an act of self defense. What an azzhat!
I read that a small group of militant Muslims got Piglet from Winnie the Pooh banned at their office in England because they hate pigs. Those azzhats don't seem to realize that their holy book says that they only should not EAT pork but nothing about children's cartoon characters.