I Am really means Awareness Is, but what it really really means is that only awareness is. Whatever you can point at or touch or think or feel or give name to, knowably does not exist. That’s the dreamstate killer. Neti neti. Not this, not that. 

All appearance — the entire dreamstate we call reality — is false. It does not, in truth, exist. There is no underlying reality to reality. Explain that apparent paradox however you want, but if there’s anything left when you’re done, you’re not done. The only thing in the dreamstate that actually does exist is the dreamer, but the dreamer is not within the dreamstate, the dreamstate is within the dreamer. The “I” in I Am is not Sue or Sam or Betty or Jed, it’s the only thing that actually does exist — the sole beholder. We are the sole beholder, not its children or emissaries or minions or clones or offshoots. It is me and I am it. There are no parts or subsets of the infinite, only the truth of one and the illusion of two. There is nothing more or less than one. The only thing that actually exists is consciousness, and that thou art.