In common usage, illusion means an erroneous representation or belief about reality. The illusion is caused by something quite real which is not however seen as it is.
The word has diverse special usages in esoteric material. Specially Eastern systems of thought deal with the concept of illusion. We'll take a few examples:
'All is illusion,' is a common Buddhist dictum. If we think of the universe as a connected whole, then any perception which is not the perception of the totality is by definition an illusion. As long as something is veiled, the human will have the tendency to take the part for the whole. 'Only the sea of Samsara is real for he who swims in it.' The Buddhist idea of suffering arising from attachments is related to the idea of illusion. Suffering, which is quite real at the level of the sufferer, has its basis in the sufferer falling for the illusion that the object of desire or attachment be a source of fulfillment. As long as one is attached to the mirages of the phenomenal world, which are all illusions by virtue of the fact that none of them is the objective contemplation of all which is, one chases shadows and accordingly suffers. Direct knowing of the objective nature of things, i.e. enlightenment is the only escape from chasing one's tail. This is however not an intellectual representation, even if this were a fairly correct one for its level, but something of a fundamentally different nature.
The idea of all being illusion should not be interpreted New Age style as stating that all is simply an artifact of one's subjectivity. One cannot learn to fly by saying that gravity is illusion. All may in the end be consciousness but one needs to distinguish between levels and degrees of consciousness.
We could say that the scale of densities correspond to a matrioshka of illusions nested inside each other. This is so because perceptions proper to the next higher density would be somewhat speculative or exceptional in the lower one. Still, within each level exist rules and laws of nature which are objective and real within this level. We should not confuse limits of perception with misperception of the perceptible due to wishfulness, laziness or naivete.
Another common use of the word illusion is in 'illusion of separation.' This means that all is in fact one but people misperceive themselves and others as separate. This is a bit of a misnomer since perceiving entities as effectively separate is even needed for reasonable functioning at the human level. Yes, from a certain point this separation may indeed be illusory but from the human viewpoint it is quite real and claiming it to be illusion only is itself propagating a deeper illusion. When speaking of illusion one must keep in mind differences of degree and situational context. Being too black and white or categoric on the matter leads to absurd statements clearly in conflict with first hand observables of the human level. Again, the purpose of esoteric development is not denying the world but rather a deeper understanding of it.
The Cassiopaea material generally suggests that a soul's degree of development determines its perceptual range which in turn determines the manner of its interaction with the world, i.e. density. This is an objectively real quality of an entity and not a matter of the entity's belief or thought.