...Four Theories:
1)To restore balance (A.K.A. Destroy the organazation and the dusk, thus making it only light and dark again.)
2) Protect Sora from the organazation. (I'll post explanation for this below)
3)To restore his memories (I'll post explanation for this below)
4)All of the above. (XD)
Explanation for 2) My idea for two is that the organzation has a way to control peoples minds, or certain ways to lure people in, mostly keyblade wielders and strong warriors. With keyblade wielders the unknowns could either use their power, or absorb the keyblade wielder's power to further research hearts. (Still working on that theory)
Explanation for 3) My idea is that BHK has lost his memories, permanantly, (explains him talking to namine), and he remembers only blips of things, such as twilight town and such. And since there's the theory that all keyblade wielders are connected, sora will remember twilight town. (Explains twilight town card in CoM) and BHK might even remember sora, thus him chasing after sora. However, this does not entirely explain why he chases after dusk...