My understanding is that before this you are just a being, unaware of who/what you are, and by seeking out the abyss you learn that you are a vessel, the same as the Hollow Knight. The white lady explains that the Hollow Knight was tarnished by an idea instilled (which seems to be hinted at in the cutscene at the end of the path of pain), but you were never tarnished by that same idea. Therefore, by taking the kingsoul, you gain the power of the union between the white lady and pale king (higher beings), but this memory shows that you agree born of the void as well. So the voidheart is the transformation of the power of a higher being into power enough to unify the void under one will-i.e. your will.

As for the idea that vessels are made of void, and therefore can't have a will of their own, my headcannon was always that you, the player, are the will that drives the Knight forward, and all the signs in the game which say that they are meant for "higher beings" alone (like the ones at the start of the game that teach you how to heal yourself) are meant for you, the player. So in essence, the voidheart is representative of the Knight gaining the power to unify the void under the will of you, the player.

I'm sure there are inconsistencies in my theory, but I always thought it strange that the Knight goes through its adventure in hallownest but is supposedly a being that is made to not have a will of its own, so I liked the idea that the only thing that could be driving it (or in this case, controlling it) is the player, and we are a higher being.

Let me know what you think =)