"Organic" used in a social context describes a situation that happens naturally and with ease, such as an interaction between two close friends or two people with good chemistry.
A: Hey, you were talking to that person for a while, how did it go?
B: Yeah I just walked over, said hi, and everything was organic after that.
C: Dude, bro, why don't you go talk to that girl? I think her friend is hawt.
D: No can do, man. It just doesn't feel organic.