This is generally because they are too shy to talk about it to each other.
Girl 2: Yeah, they should def. move on from their skinny love...
guy: but i don't know how to be single again!
The first is used to describe a type of relationship between two people that are very in love with each other, or are crushing big time on the other; but are far to embarrassed to express their feelings. The relationship is 'skinny' because they have yet to come out and explain their true feelings. There is no communication, there for it's not even really a 'relationship'.
The second is to describe a similar thing, but instead of no communication, the relationship lacks love. It is where two people are dating just for the sake of dating, the sake of being with someone. To fill that empty void, to give them something to do. They do not actually love each other.
Samatha: Aw how sweet! Jimmy and Kira look so cute together. It must be true love!
Kira's friend: Yeah, but they are always too shy to tell each other that they love them. It's skinny love.
Karen Gillan: "Matt has a massive crush on me."
'Who's Matt's celebrity crush?'
Karen: "I don't really know."
Matt: "I'm going to say Karen Gillan."
Karen: "Matt's a superb kisser."
Matt: "I'd give Karen a 9 or 10 for kissing."
Interviewer: (to Karen) "but you're so pretty!"
Matt: "Thanks! Thanks buddy!"
This ladies and gentlemen is a very good example of Skinny Love. As you can see, Matt and Karen are definitely in love with each other but they are not in a relationship.