Apologies if I'm repeating myself, I just can't remember. ;-) For a very physical explanation of consciousness go here.
I do my best thinking in the bathtub. I think it has to do with the water, which is the most prevalent and vital substance on our planet. And the fact that we call our consciousness a "stream" is significant because it suggests that our consciousness is like water in the way it behaves. I like this metaphor. I like that it implies our streams are only part of a larger network of something in the same way that water streams, rivers, and oceans (as well as clouds, rain, fog, etc.) are all the result of water's behavior on our planet. What makes this a metaphor and not a real analogy is that we really don't know how consciousness behaves other than what parts of it we can study within the brain's activity.
I wrote a much longer bit about stream of consciousness, but because I've been feeling really stupid lately I decided to leave only a little drop of it here. The rest is still in the reservoir.