The relation between Inori and Shu is the begin and the meaning of this series.
He starts like a student that doesn't like his life, and that lives it hating the situation in which the world is because of a tragedy of ten years ago, called Lost Christmas. From that moment, a cancer started to kill people, and because of it, many friends of Shu had a lot of problems.
The meeting with Inori changes his life, because finding her, finally he found a person that doesn't care about words, she says what it needs to be said. She can be kind, or evil, or sarcastic. But she always try to let Shu understand that his life is a shit because he's the one that is not doing anything to change it.
Day by day, starting to control and use the void of Inori and everyone else, Shu understand that he can do a lot for the world, and thanks to Gai's support and Inori's presence, he changes himself.
There are difficult moment in which Shu thinks that he's losing all the important things (as Hare's death), but until Inori will be near him, he'll have the stregth to go on.
Inori's hand is what he needs, and Inori never leave his side, because she's his partner and his most important thing~

I adore this couple, the development of the relation between Inori and Shu is so sweet, and many times sad, because of the sad situations of the series. But they're always able to overcome their limits, and together, they can face life and try to save the world from cancer.