the beginning
Kairi starts life in the Kingdom Hearts games as still a child. She's not really hit too much of a teen stage, though does have some obvious teen atributes. She's a bit more of a rebellious, laid back kid who gets out of work when she can. She is very unsure of herself. This is obvious, due to the fact she is usually laughing after every sentance. She says something, and giggles nervously - this is probably as she hangs out with Sora and Riku. They are boys, afterall. She would be nervous around them. She'd probably also be nervous due to the fact they're childhood friends and she doesn't want them to think she's strange or weird for being a girl.During the course of the first game, we don't really see her change much, as her heart is within Sora, and we don't really see her till right near the end. But maybe this little visit to being with Sora and the other princess' hearts was significant. When she 'woke up', she was a lot more sincere. Her nerves and naivety seemed to had gone. She was lot more sure of herself, and sure of protecting Sora was the right thing. She even protects - albeit feebly - Sora, which is a big change from the girl who needed protection right at the start. She's done a lot of growing up in that time. She's a bit more stubborn as well, though mostly takes what Sora says after some persuasion.
Within COM, Kairi doesn't appear directly. But in the half year/year gap we have between COM and KH2, she has done a lot of growing up. She's kind of skipped the teen years and gone straight to a young woman. She's been forced to grow up. Her nerves are gone, she's a lot more sincere, and seems to have gotten in touch with her feminine side a bit more than before - having some of her tomboyish-ness melting away. She's a lot quieter than she was before. She seems to get sad a lot easier, too.
Even though through that, she is still pretty outgoing and a lot more rebellious than before. When Axel comes to get her, she listens till running off into the unknown - not exactly a wise move, but Pluto was leading her places. She makes friends with the Twilight Crew pretty quickly, as Sora usually makes friends with everyone in the space of five minutes. Nearer the ending, she seems to show knowledge, seemingly knowing more than she lets on. Though worries about Sora a lot, and still gets captured. Not much change there. All in all, Kairi is a bit more independant having spent so long by herself, and seems to care about Sora more than ever.