The Debt of Tears is a concept presented in the very first chapter of Cao Xueqin's Dream of the Red Chamber. It occurs in a dream that a seemingly minor character, Zhen Shi-yin has, and although it explains one of the major plots of the novel, relating it to the actual interactions of the characters can be difficult, if you don't know exactly what to look for.
In his dream, Zhen Shi-yin hears a tale of how in the fairy realm, The Stone, the sentient spirit of a magical rock, lives in the court of the Fairy Disenchanment. While walking around her realms, he finds a special flower, the Crimson Pearl Flower growing. The Stone takes a liking to this flower, and waters it with magical dew every morning, which (considering the flower is already magical) leads to the flower growing into a human form. As a fairy girl, the girl lives in the fairy realm, but gradually realizes that she owes a karma debt to the stone that watered her. She believes that the only way to repay the stone is that if both of them could be reborn as mortals, she would shed a lifetime of tears over him.
It isn't until quite a few chapters later that the major chacters in the work begin to be introduced, and it can be dozens of chapters in before the reader starts realizing the dynamic between them. And indeed, the dynamics between Jia Bao-yu and Lin Dai-yu don't become entirely clear until at least 3/5th of the way into the 2000+ page work. However, with some reflection (and perhaps a Professor of Literature to explain it for you) it is clear that Bao-yu, the petulant but caring scion of the Jia household is the Stone, and Dai-yu, his cousin who he loves is the flower. Although they love each other, and want to be together, the mechanics of family politcs (and their own problems at communicating) keep them seperated from each other, and in the end Dai-yu (who is a rather tender soul, in any circumstances) dies of heartbreak after realizing that she can't have Bao-yu. But before she does this, she cries and cries for months, giving back all the water that allowed her to take mortal form in the first place.
I think the concept is very romantic and beautiful, despite its morbidity. I have to admit that it does leave me thinking often about what exactly the relationship between myself and a few women I know could have been like in a past life that has caused me such sweet grief in this one.