One thing I know is that there is no physical law I've ever learned about that accounts for it. My brain is doing information processing, and the connection between that and physical laws is clear. But it seems like that could happen entirely without the accompanying subjective experience.
On the other hand, it has to be somehow connected to the physical, because my consciousness (temporarily) goes away when I sleep, and an anesthesiologist once used chemistry to force it to go away in about 5 seconds.
And I have no idea how to reconcile these two things. I've heard "it's an emergent phenomenon", but that's super hand-wavy to me. It might be true that it's emergent, but that doesn't tell me what the connection is. Plus emergent consciousness is not a very falsifiable hypothesis since it conveniently says don't be surprised if you never see anything at all if you look for it under simple conditions.
Anyway, what is an emergent phenomenon? In terms of numbers, I'll say it's like if you start with X which is tiny, then multiply it by 1.01 a whole bunch of times, eventually you'll get a number which is significant. That makes sense, but it assumes X is nonzero, and the most interesting question is why X isn't zero.