- a thing that is or is likely to be wrongly perceived or interpreted by the senses
- a deceptive appearance or impression
- a false idea or belief.
Daniel Dennett in Consciousness Explained lays out his argument for how consciousness is illusory by starting with debunking Cartesian duality and concluding with an assessment of Searle's Chinese Room and addressing Nagel's What is it Like to Be a Bat? among others. Obviously any characterization of argument made over 450 pages reduced to a few paragraphs would be liable to be misleading, however:
What Dennett highlights in his book is that the uniformity of the conscious experience (what is known as the phenomenological) is itself a composition of many distinct processes that can be teased apart in heterophenomenolgical discourse. This is nothing more than what might be characterized as people sharing and reasoning through their experience as a group presuming that an individual's experience is not authoritative. This is, of course, is an accepted tenet in legal or scientific reasoning.
In fact, what Dennett repeatedly does throughout the book is to show how science, be it that of psychology or computers, shows that the human brain is composed of many subsystems that can be reasonably understood as a computer. Using these facts, he then makes an argument that subjective experience is actually a composition that doesn't neatly align with physical reality, but is rather a construction that resembles a virtual machine and that entities, properties, and relationships as traditionally perceived in philosophy fall short. He uses color as a prime example.
"Objects" don't have colors. The sky, for instance, isn't really blue. The "blueness" of the "sky" is an illusion, because "blueness" and "sky" as our subjective experience is concerned are constructions of the mind. This is not to say that EM waves don't have wavelengths, or that the "sky" isn't the atmosphere as we understand it heterophenomenologically, but rather our phenomenological experience isn't what reality is. George Lakoff and Mark Johnson call these "transactional properties", which are understood to be neurocomputational structures which associate the physical with the mental. (See Philosophy in the Flesh.)
It's a well accepted fact that your conscious experience is vulnerable to illusion, confabulation, bias, fallacy, and deception from others. To claim that consciousness is an illusion is merely to concede these, and provide a philosophy of mind that is compatible with materialist and physicalist thinking. In essence, to claim consciousness is an illusion is merely an attempt to reduce the qualia and a holistic interpretation of subjectivity to intersubjective and reproducible processes. It's an attempt of those with positivist and analytical roots philosophically to create an operational definition as other people's awareness is not directly accessible by our own (as per the problem of other minds).