"To give a damn" means to care, be concerned, or have interest in something or someone.
Sentences with «to give a damn»
I am Catholic... well, let's say I was born Catholic... am not really religious and don't give a damn about what the church says. (religion.blogs.cnn.com)
I don't give a damn about who's out there. (onefootdown.com)
I don't give a damn what anyone thinks about me, I don't try to impress no one and never will. (cowboymate.com)