1) A fig newton is a noun that defines a relationship that is more than just being "friends with benefits." You have sex but you actually have feelings for each other, you are emotionally dependent on each other but it's not (yet) love, and for some reason (i.e geographical distance, availability, commitment issues, etc), you two have chosen to not be in an exclusive relationship.
2) A fig newton is for a relationship you have with someone that you cannot categorize as "just friends," "fuck buddies," "friends with benefits, or "boyfriend/girlfriend."
"Oh, he moved to NYC. We still have feelings for each other and have sex when we see each other though. But we're not in a relationship or anything"
"What do you call those things?"
"Oh, he's my fig newton (n)." or "We're fig newtons (pl)"