My favourite explanation of consciousness currently is Integrated Information Theory.

And one prediction that theory makes is exactly what you write, @kevinwong, about how a being's measurement of consciousness is in proportion to the number of neurons that it has.

It's not easy to understand or explain, but you can read more about it here:
https://en.wikipedia.org/wiki/Integrated_information_theory

Or better still, watch this great series of YouTube clips with Giulio Tononi who proposed the theory:
https://www.youtube.com/playlist?list=PLMDgR9XqmpVT7ZJVKc_N0oKdEV3Aq7cFS