The abridged story of KH:
Sora, Riku, and Kairi live on Destiny Islands. They suddenly get a wonderful idea to leave it and visit new worlds. Conveniently, a storm arrives that takes them to new worlds, but when Sora arrives at Traverse Town his friends are nowhere to be found.
-Stuff happens-
Ansem, the villain of the game, is revealed to be inhabiting Riku's body. Using Maleficent as a pawn, Ansem gathers up six of the Princesses of Heart in an attempt to open the door to Kingdom Hearts, the heart of all worlds. At first it's never explained why Ansem wants to do this, but later we find out that he's a heartless (creatures that eat hearts), so he was probably just hungry.
Anyway, Ansem finds Kairi, who turns out to be a princess of heart. However, her heart is missing, and it's- *PLOT TWIST!* inside of Sora. After defeating Ansem and taking his keyblade that unlocks hearts, Sora stabs himself, freeing Kairi's heart and becoming a Heartless himself.
By becoming a heartless, Sora in the process makes a Nobody, Roxas. See, in the world of KH, there are 3 parts to a person, a heart, a body, and a soul. When they're all connected, you have a human. A heart separated from the other two parts is a Heartless, and a Soul and Body separated from the heart is a Nobody.
Kairi is able to give Sora a new body (somehow), but he's really just a heartless with human form.
-Stuff happens-
Sora is eventually able to catch up with Ansem right before he reaches Kingdom Hearts. He defeats him, freeing Riku (almost) and saving Kingdom Hearts.
KH
ays starts 1 week after Sora becomes a heartless and creates Roxas.
If you have any more detailed questions I'll be happy to answer.