The illusionary creature (幻想生物 gensō seibutsu) is an illusion of the Blue (蒼の幻想 Ao no gensō), created via Blue from human desires, malice and fears.
In BlazBlue: Bloodedge Experience — Part 1, Raquel Alucard said that some time in the past, someone touched the Blue and created an illusionary creature with it, that creature being Clavis Alucard. His existence itself is like a Drive.