The Illusion in question is religion. Freud's book is a discussion in essay format about the future of religion given the progress of psychology and philosophy. He starts by explaining the religious experience and the phenomenon of religion. Obviously, the experience of religion is one of the most consistent phenomena across the planet. His answer is that religion is an expression of the human wrestling with their complex reality in the ways native to their perception; they desire a God who gives life meaning by embodying a father who can be trusted.
He explains that religion is an illusion in his opinion, because religion involves the construction of meaning from an experience that seems to fit that construction; but that doesn't necessarily imply anything about truth or falsity. Rather, it seems to imply that a human has the power to make things religious by understanding them through that lens. He claims that the question of religion is not to explore the truth of the universe, but to explore the human nature, using the lens of religion. This makes religion an illusion because it involves the experience of mis-perception; the religious person believes they are discussing God when they are really exploring their own capacity for religion.
He continues in his arguments to discuss his famous theory of the Oedipus complex. Given man's inherent powerlessness in reality, that man might experience a longing for the safety of the maternal experience. He explains how this experience can become complicated by a growing psyche, so that the sexual urges of a person are also wrapped up in this desire for absolute care and safety. He says that the need to be involved in a parent-child experience with God is essentially the Oedipal complex being played out on an existential level. The realization of this illusion would be horrifying to anyone brave enough to face the true horrors of suffering and death, without the crutch of religious belief.
