A Light In Dark Places
First and foremost, the game has established time and time again that Sora harbors romantic feelings for Kairi, and vice versa. This is not ambiguous; rather, it is implied in a very different way. The evidence ranges from small incidences like Riku teasing Sora about sharing a Paopu fruit with Kairi, to outright obvious dialogue. For example, Saix asks if Kairi is that important to him, Sora replies, "Yeah, more than anything." Similarly, when Saix poses the question to Kairi about wanting to see Sora, she in turn says, "I do, more than anything." With that, a key point to remember that when they share their feelings towards each other, it is not said by words, but shown by actions. More importantly, however, throughout the series, it has been pointed out that Kairi is Sora's light. This might be an obvious statement in that Kairi is one of the Princesses of Heart, whose hearts are void of any darkness and only made up of light. However, I believe there's a bit more to it than that.
Perhaps one of the more famous moments where Kairi and Sora share the screen is when Kairi summons Sora back from the darkness, after he had turned into a Heartless. Sora had unlocked his heart in order to free Kairi's, which was contained within his own the whole time. After Sora had unlocked his heart in order to free Kairi's, she had awoken, only to find Sora's form dissolving. Unable to save him, she tries to escape Hollow Bastion, only to be tailed by a heartless. Unremarkably, she recognizes Sora in his heartless form, and protects a helpless Sora from the ambush of other heartless. Her embrace returns Sora into his human form again, thanking Kairi for watching over him.
Kairi, being a Princess of Heart, had used her light to purify Sora in order to restore him. However, remembering the special connection they share with one another, Kairi's embrace had, in essence, only reunited Sora's heart together. If Sora had the ability to contain Kairi's heart, then the same, theoretically, would apply vice versa; Kairi had a piece of his heart, as well. Sora had been falling towards darkness, and it was Kairi, his light, who brought him back by making his heart complete again.
In Chain of Memories, Sora discovers that as he ascended Castle Oblivion, Namine began to successfully replace the image of Kairi in Sora's memories. His feelings for Kairi were so powerful that they could not be erased; instead, Namine rearranged and rewrote the memories so that the feelings would still exist. Though the image of Kairi may be different, the connection between him and Namine still belonged to Kairi (and with that, Namine is still a piece of Kairi-- her Nobody, to be specific). As Namine confronts him about this endeavor, she agrees to restore his memories. But before she can do so, he asks him to remember something very important; something so important that even he could not forget completely.
"But there's another promise you made--a promise to someone you could never replace. She's your light. The light within the darkness"
-- Namine, Chain of Memories
As Sora begins to remember Kairi before he sleeps, his memories of everyone he had forgotten resurfaces. Kairi is his connection to the real world-- of reality-- of things that happened and feelings that existed.
Previously, Sora had gained hold from Riku a specific Keyblade that was composed of six hearts, which belonged to the then-in-a-coma Princesses of Hearts. This Keyblade was special in that it had the power to unlock people's hearts. While in Hollow Bastion, Sora had tried to lock the keyhole, but all seven princesses needed to be awake in order for it to be complete and lockable. Sora, knowing that Kairi's heart rested within his, got an idea. With Donald and Goofy protesting, Sora picked up the keyblade that unlocked hearts, and with a smile shot at his friends, unlocked his own. Because the dark keyblade was being used with pure intentions, it dissolved into the princesses' hearts, and at the same time, Kairi's heart returned to her body.
I believe that this is one of the most significant events in the series-- once Sora had figured out the last piece in the puzzle; he sacrificed himself without the slightest hesitation. This unselfish sacrifice, for Sora, is character defining; it is the reason why Sora's role is so important. Sora himself doesn't exactly know why he has the strength to overcome even the most powerful force of darkness, but it is this particular moment where we find the answer hiding in plain sight: it is the understanding that love endures because it saves people from the darkness when there is no other option left.
"Think, Sora. Think of the person who's most special to you. See that faint glimmer way in the back of your heart? That's a piece of your memory, Sora. Call out to it! No matter how far away the light gets, your heart's voice will always reach it"
-- Namine, Chain of Memories
The powerful message that is relayed to us from the story is that, within each and everyone one of us, there is a light that never goes out. For Sora, the light at the end of the tunnel isn't necessarily just Kairi; it's the feelings he has for her that keeps him going. Of course, the capacity to love is held within each and every one of us. Thus, light, in its purest and simplest form, is love-- love is precious, unselfish, and real.
"Of all fires, love is the only inexhaustible one"
-- Pablo Neruda