I am not sure I can, strictly speaking, observe my own consciousness. I have the sensation it is there, but that's not exactly the same thing. I can't observe other people's consciousness, only deduce we're all similar due to that being virtually logically necessary and completely obvious – so I think it's fair to say I can't observe myself any better. While I can report sensations and qualia, I don't have much of an inside track on actual facts about my brain, in the same way I cannot meditate on the nature of a gallbladder for insight.
If there is no technical process that produces consciousness (and, for instance, no computer would find itself in this category), it's worth saying, it is a fairly persistent qualia. I am myself literally all the time, even when I'm so engaged in something I don't give any thought to myself. I still have a quazi-narrative connection to my actions – I did the work I was so lost in, for instance. Even if you zone out, you're still the one that drove home.
It's worth mentioning two distinct ideas that might be a pointer towards plausible guesses – that consciousness is the qualia that exists to connect short-term narrative memory, fleeting thoughts, our changing feelings, and our other ephemera. These actual processes are most useful when connected together, and so we have an experience, not unlike the experience of a memory, that connects things – but this connection itself isn't a mechanism, or isn't the mechanism we would acknowledge as being, in any way, profound.
The other is that consciousness is the instruction pointer of the mind. It needs a part of it that points to what it is doing, and that is a very real and physical part of the meaningful processes. Consciousness not only exists as a part of the physical nature of the brain but also includes all modern computers and probably confers no information about ethical value.
Of course, other people have already discussed the idea that it is unlikely to be supernatural - if it's not related to any physical processes, we should be a bit disturbed that the physical processes in our brains cause us to open our mouths and share these similar experiences. I shudder to think the nightmare if the "merely" physical process would get it wrong, and our consciousness is trapped in a system incapable of reflecting it at all.