Your confusion is understandable
That we are conscious, appears to be innately true. If one wants to build a model of our world, then one needs to start with experiences and perceptions, and build out from there. This is the basic foundationalist approach to understanding our world, and the undeniability of consciousness is intrinsic to this methodology.
But philosophy is often complex, and subtle
HOWEVER, philosophers of science have realized that "Theory is always underdetermined by evidence", IE every theory can in principle accommodate all apparently refuting evidence, if one constructs a sufficiently complex rationale or justification for doing so. And this is also the case for consciousness.
There are two categories of thinkers I have encountered who reject the reality of consciousness and selfhood. Both start with a worldview, and the dismissal of consciousness as a delusion is based on the assumption that the worldview is correct, and the dismissal of the APPARENT evidence of consciousness is fully justified by the necessary "truth" of the world view.
Non-duality asserts delusionism
The more venerable of these views is that of non-duality, in the Vedic tradition. The most common version of this view holds that reality is consciousness, and that there is a single consciousness that creates everything in the universe. And while we think we are different consciousnesses than the Mind at Large, we are mistaken -- we actually spawned off of MAL, and when we overcome our delusion of separateness, duality, we will re-merge into MAL.
Variations of Buddhism take this thinking even further and declare that consciousness/non-consciousness is another false duality, and the fundamental nature of our universe is nothingness, not consciousness.
WHY we have these delusions -- why they are stable and seem to be useful -- is not something I have never seen a good explanation for from non-dualists. The thinking is, instead, that mystics have discovered the true non-dual reality, and THAT we are deluded is a fact. Explanations for why that fact may happen to be stubbornly denied by people, are not as important as that it is "real".
There are also materialist delusionists
The second set of delusionists I have encountered are much more recent. They are a set of materialists who have realized that the "hard problem of consciousness" has resisted over a century and a half of materialist efforts to resolve it, because it cannot be resolved. Their approach is:
- Materialism has been shown to be true of our world
- The hard problem of consciousness cannot be resolved in a materialist model
- Therefore, the reality of the data of consciousness must not be valid, because materialism is more trustworthy than consciousness
There are at least four good references for this POV. The dean of the movement is Daniel Dennett, and his very dense "Consciousness Explained". A second leader is Daniel Wegener, with "The Illusion of Conscious Will". A less dogmatic summary, that doesn't offer a worldview, but implies one, is David Eagleman's "Incognito". The absolute best of this set is the last, and shortest: Blackmore's "A Very Short Introduction to Consciousness". Blackmore explains the empirical data that refutes all of the materialist models of mind, and explicitly (rather than implicitly, like Dennett and the others) argues that because materialism is certain, that must be dismissed. I review Blackmore here: https://www.amazon.com/gp/customer-reviews/R1C1TJFIWBZ8ZQ/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0198794738
While this may strike many of us as a very implausible argument, the Delusionists cite a fair amount of evidence to show that we are often very WRONG about how our consciousness works, and that illusions, delusions, fill-in, back dating, and flat out lies are features of what we tell ourselves about our consciousness. The inference that ALL of consciousness is a delusion, rather than just subsets of it, is a leap well beyond their data. But the argument that subsets of it are delusions DOES thoroughly savage any "we MUST trust the truth of conscious experience/claims" arguments. NO we can't trust our consciousness!!!
Dennett's model is that we are basically unconscious meat machines, and that the illusion of consciousness is created as an accidental byproduct when our self-machine writes its short-term memory into long-term memory. I.E. we have a created, and backdated MEMORY of being conscious, but never actually were. He holds that our meat-machine selves use that memory for interpreting the past and planning for the future, so the backdating and illusion are important to our algorithmic self to maintain a time-valid model of our past, to project into the future. This is a complex model and is an example of how ANY theory can be reconciled in principle to any facts with a complex enough kluge.
However, Dennett's model leaves out a major question -- "WHY would the backdating etc. involve the creation of qualia and experience, when they never happened in reality?". This is a slightly different restating of the Hard Problem of Consciousness, and Dennett does not have an answer, which actually leaves him too, unable to address the Hard Problem. Blackmore's simpler solution "we aren't conscious" is the cleaner approach for materialist Delusionists.
Now to answer your questions
So much for the background, now to your questions:
- What does the statement "I am conscious" mean?
Its meaning, for delusionists, is that one is still enmeshed in the delusion, and the statement is simply false, but the speaker does not realize this.
- Is it also in the view that it is illusion that I am conscious?
Yes, all of these views would hold that selfhood, "I", is an illusion. And all but the Mind at Large thinking would hold that not only is your consciousness an illusion, but so is all consciousness.
- Is it possible that one is in illusion that he is conscious, but actually he is not conscious?
Yes, for the Buddhists. They hold that we are not conscious, because nothing is. The other Vedic hold that "he" is the illusion.
Yes also for the Delusionist materialists.
- Can consciousness be illusion as some philosopher, in more details hold a position, and explain it?
I tried to summarize the explanations. They are coherent. They may not be convincing if one does not accept that their assumed worldview is correct.