CIRGAF stands for 'Cuz I Really Give A Fuck.
This is used in a sarcastic manner, and is used to tell the other person you could truly care less about their topic on their conversation.
You can use CIRGAF to truly tell the other person to GTFO, or you can use CIRGAF towards people who don't know what it means to just say "Don't worry about it. Continue." Just so you feel like you made your opinion.
Also refer to Sir Gaf.
"Hey man, I was at this party, and I was getting drunk, and I met this girl.."
"Hey man, wassup. I got an A+ on this super hardcore test that my teacher gave me, and I was like..."