This is most likely the best video I have EVER created on Vegas. I mean, I'm surprised on how well this came out. There's a story too, which makes this all the much better. Well I dunno, but here's a story on their relationship:
Since both Kimimaro and Rin were originally from the same village they were old friends, despite Kimimaro being in a cage for most of his childhood. Every so often Rin would come down to visit Kimimaro, because their clans were actually allies. Because of this, Rin was easily allowed to see him, which gave Kimimaro something to look forward to.
After the news that the Kaguya clan was completely wiped out Rin was devastated (sp?), this made her jump to the conclusion the Kimimaro was also killed. Rin knew she liked him, but she also knew deep inside he just wasn't gone yet.
Years passed and Rin slowly started to let go of Kimimaro, almost forgetting him completely as she made her migration from Hidden Mist to Hidden Darkness. Kimimaro on the other hand, even though completely devoted to Orochimaru, never actually forgot about his only friend from the past.
During the currents of Shippuden (after Kimimaro's death in battle, which Rin was never notified of) she pulls out an old notebook from her belongings that Kimimaro and her used to pass notes when the guards were watching. She smiled, now remembering what she had almost forgotten completely. She didn't know he died 2 or so years ago, but she knew she had to find him somehow. To show him that even though she let go, she still remembered.
While all of this was going on, Rin was also studying a new jutsu that only someone of her power level and chakra control could actually manage. There was a high chance she could even kill herself in the process of performing this jutsu, but it was traditional for every Asamoya spirit holder in her clan to learn it. This specific jutsu was called: Ikikaeru no Jutsu. The ability to revive one back to life, reality, even if they have been laying dead for years.