You may well ask how consciousness can be an illusion, since every illusion is itself a conscious experience—an appearance that doesn’t correspond to reality. So it cannot appear to me that I am conscious though I am not: as Descartes famously observed, the reality of my own consciousness is the one thing I cannot be deluded about. The way Dennett avoids this apparent contradiction takes us to the heart of his position, which is to deny the authority of the first-person perspective with regard to consciousness and the mind generally.
The view is so unnatural that it is hard to convey, but it has something in common with the behaviorism that was prevalent in psychology at the middle of the last century. Dennett believes that our conception of conscious creatures with subjective inner lives—which are not describable merely in physical terms—is a useful fiction that allows us to predict how those creatures will behave and to interact with them. He has coined the term “heterophenomenology” to describe the (strictly false) attribution each of us makes to others of an inner mental theater—full of sensory experiences of colors, shapes, tastes, sounds, images of furniture, landscapes, and so forth—that contains their representation of the world.