Illusion is a status affliction unique to Dimension Number 2. Any affected Pokemon will see hallucinations, other Pokemon in weird places or positions, and so on in a perpetually twisted perception. The effects can drive a Pokemon insane in the course of a few minutes. Fortunately, the effect usually only lasts about 5 minutes.
It is believed that some Psychic-type attacks, especially after a critical hit, disorient the mind of the victim so harshly that they take on Illusion in place of Confusion. Also, some items have a small chance of causing Illusion.
Illusion can become contagious, as well, but only if a Psychic-type Pokemon contracts it. Any such Pokemon with Illusion status has a very high chance of spreading it through their own Psychic-type attacks; that is, if they can get it to hit successfully.