Yes, there seems to be a wall in our ability to understand what it is but here are some things to think about
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1) Consciousness doesn't seem to be tied to matter specifically. The atoms in your body are replaced all the time. Though consciousness might be tied to the general structure of the brain and disrupting this structure too quickly might not allow consciousness to retain a hold ... just a possibility ... like you can slowly bend some things but if you do it too rapidly, they snap.
2) I think there's a lot of evidence that consciousness is connected with the quantum "noise" we see in everything. I've read some other research along these lines and there appear to be very very fine arrays of structures inside most all living cells that could provide a mechanism, like an array of radar dishes to coherently detect quantum energies.
Something interesting is that single celled organisms can swim gracefully, eat, mate, avoid preditors and seek out food, all without the benefit of a single neuron! That's rather impressive considering humans even have a tough time doing half those activities.
The interesting part is that though they lack a nervous system and are only single cells, they still contain elements of this fine array of tiny structures. The hypothesis I read was that they cold operate along the lines of a laser tuned to a specific frequency by synchronized firings along this array, so this could provide a mechanism that's "tuned" to communicate in a certain manner.
3) Free will is an interesting subject that could differ from consciousnss. Perception and action might be separate components of consciousness. I used to think the universe could repeat over time, but this has some problems - 1) if it repeated, that would mean no new information is being added to it, which would mean free will is only an illusion but I don't think free will is only an illusion not simply because it doesn't appear to be an illusion, but there was some creative force that had to at least have been present once to create the universe we currently experience and that must have always been present, and my guess is that it likely still is continuing 2) Also, life can only be experienced by changes. If things simply repeated, you could view the entire span of existance as simply a rigid crystal. There would be nothing to differentiate one moment from the next. Some new input is necessary to keep things evolving and allow changes to exist and be sensed. To me, this implies a form of "free will" outside the existance we experience that's effectively the energy source (likely limitless) driving these changes. My guess is that the expansion of the universe will prove to not be a one way trip to a cold and lifeless universe but representative of a continual growth (evidence seems to point toward a trend in this direction - everywhere we look, there's always more detail).
4) There's a lot of evidence pointing toward the brain not simply operating as a network of discrete neurons, but as having holographic traits with waves of information propogating through it being correlated with other waves passing through it.
I bring this up because there seems to be other characteristics to the universe that operate along these lines also. It's possible there's much more interconnectedness in a large number of things, including consciousness than we really understand. (Maybe "intelligent design" is the only thing that exists in the universe?)
5) Consciousness has traits that appear to be discrete and digital instead of analog and continous. Our attention jumps between things instead of smoothly glading around. There might be two states involved, possibly perception and then action.
Something not too obvious about consciousness is how it actually observes a very compressed set of information. You might look at a tree and think you're seeing all of it, all the time you're looking at it, but actually most the tree you're perceiving is more of a sense of the general tree "texture" or characteristics. Consciously the mind tends to follow specific thoughts and you really one perceive a small amount of information in any specific moment of time - though when you refocus your attention elsewhere new details are extracted, so subjectively it appears that you're able to perceive all of it at once, but that's not really true. Even people with a photographic memory don't actually perceive the entire tree, they're simply able to store it (likely physically in the brain somehow) and then later go over this image consciously and extract information from it.
I say this because l think an old analog modem probably has a higher bandwidth than our conscious perceptions. The difference is that we have incredible mental algorithms for compressing a lot of data into a small available channel of information. (If we had compression algorithms that good for a DVD, you could probably fit 100 movies on a single disk).
6) Likely a large part of what we perceive as consciousness is due to the operation of the body and the brain. Consider that probably most people think thoughts in their native language, whereas language skills are likely part of the brain. There are structures we know are associated with language ... and, I've said it before, but who would envision English or some other human language as being the language of the "soul"?
One the other hand, patterns seem to be a rather universal language. There are many things that are beautiful or aesthetic pleasing and my guess is that part of this is that consciousness enjoys extracting and processing patterns and correlations. Recognition of music is partly mental, but the enjoyment of it would seem something that's part of the conscious experience. Music tends to be very mathematical with patterns.
Quantum computers have a trait novel to all other forms of mechanical computation - they can process in parallel merged sets of data quickly and generate a probabilistic result that tends to correlate with the most likely answer for this merged set - sort of like being able to calculate many things at once, in parallel and then randomly select one of the best results. This seems to correlate well with how consciousness works. Quantum computations also occur in phases (though I've heard there's some debate over this) where you expose a quantum system to a merged set of inputs and then let it settle down to the "selected" result.
From an evolutionary point of view, if quantum computations have the expected level of computation power for some problems, then likely nature would have taken advantage of this already so it would make sense that forms of life would use this.
Also quantum properties aren't specific to any particular of matter but can be passed between them as they interact, so this could be correlated with the ability for consciousness to remain "attached" to a body, though specific atoms or matter in the body are only temporarily present and are "passed through the system" over time.
Sidenote: These quantum computations only provide an advantage for some types of computations, not all. A classical computer could likely do at least as well as a quantum computer for many types of calculations.