What does the phrase "that killed me" mean?

I've heard people say "That killed me" from a few people and in older books (I'm looking at you, Holden Caulfield) and I'm not sure about it's meaning. Is it like something that ticks you off like "this guy kept insulting me, that really killed me", or something that makes you laugh really hard like "I heard this great joke today, it killed me" like a knee-slapper kinda way?