To be illusory is to give only the impression (or 'illusion') of existence. Essentially it means to be imaginary. Illusions are actually a commonplace feature of life and can be caused by distortions of any of the human senses.
For example, illusions are used by magicians to have you believe in their magic tricks. Another illusory thing could be your own imagination such as seeing pictures of insects on TV and feeling the sensation of having them crawling on you.