It's just a fancy Lit-snob way of referring to a character's 'inner life', as opposed to the externally observable ways he or she relates to other characters and his/her environment (which, you guessed it, is called 'exteriority').
I would have went with: "I've always wanted to explore the interiority of a sorority."
Fictitiously yours, Trent Roman
I'm trying to come back with a line about having an "interiority complex", but I'm stuck.
I would have went with: "I've always wanted to explore the interiority of a sorority."

Fictitiously yours, Trent Roman