1. To not
care at all about something; to have no
opinion whatsoever about it. Often used dismissively in the negative to tell someone that what they are
talking about has no relevance whatsoever to the listener.
2. A humorous way of saying you are constipated, and therefore "can't give a crap."
Boss: Dilbert, that is the dumbest idea you have come up with yet. I reject your proposal.
Dilbert: You never like any of my ideas. One of these days you're going to push me too far, and I'
m going to quit.
Boss: Frankly, Dilbert, I do not give a crap.
Doctor: So,
Bill, I understand you're constipated?
Bill: Yep, doc, I can't seem to pass those poops because they're just too big. I
don't give a crap.