oral sex, whether it be consensual or not ei: "a conversation with his/her privates"
1) often used in euphemism to ask if someone would like to give you for oral sex.
2) alternatively, a covert way to inform someone that you are quite displeased with someone and would like to shove your privates into their face
1) It's kindof crowded in here... you wanna go someplace else for a private conversation?
2) Nick: What are you guys whispering back there? Is it a private conversation?
Joe: How 'bout I come up there and shove my balls in your face? Then it'll be a private conversation!!