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.
Nagel starts his review by laying out Dennett's argument, then forgets about it once the word "illusion" is used. Perhaps it would be more correct to say that Dennett says consciousness is an emergent property at the manifest level of reality and does not exist at the scientific level. It is a real thing at the manifest level.