Well, this is just what I've gathered thus far, based on what little I know:
Ven was given a new heart, that was born at the same time as Sora's. However, since the darkness of Ven's heart was extracted and used to create Vanitas, Ven's heart was missing something.
Ven said:
Yeah, my heart is missing something.
Ven realizes this, and the voice in his Awakening replies with:
If that’s the case, then it’d be okay to connect it with my heart. Thus, yours and my hearts have come in contact. The incomplete heart is healed by the connecting of two people’s hearts.
So, in order for Ven to have a healed heart, he connected it with Sora's heart.
Ven said:
Inside that child, was a familliar place, where light was overflowing…. Our hearts have a part that’s not enough, born at the same time.
So, Ven had made a connection with the boy, because his heart had not be enough on its own (what with his darkness, an important part of a heart, having left him). So, by connecting their two hearts, he was able to have a healed heart, that was essentially complete.
(This is just my thoughts, I don't know if this is how it really is)
But throughout the game, Ven's connection with Sora allows him to be an acting force and what not. Then, for whatever reason, he looses this connection (which is why he can't wake up) In the end, he asks Sora if he can join with his heart once more, and go back to sleep.
Ven said:
Is it okay if I become one with your heart again?
Sora says yes, and then Ven's broken heart connects with Sora's again, and through the two hearts, they have a healed one. However, instead of this healed heart residing in Ven like it had throughout the game, it instead went into Sora, and Ventus went back to sleep (aka the lifeless body in the Chamber of Waking).
This is how i think the connection works, based on what i know of the beginning, and the ending. But, obviously, I haven't played the game yet, so, i could be wrong.
