An Affectionship is the in between of friendship and a relationship. You are not boyfriend and girlfriend but nor are you just friends. You have a deep affection for one another but have not yet made it official. An affectionship tends to lead to a serious relationship, so hold off on the DTR and let it take it's course.
Man: Are you and Courtney dating?
Man: Kind of, I really like her but it's more of an affectionship right now.
Woman: Chris just asked me out!
Woman: So what is this??
Woman: It's an affectionship, we like each other.