Normal Illusions
When the series started, Mukuro was the first person who showed the power of illusion. An illusionist use this power to make his enemy feel, see, hear, smell things that aren’t there. Basically, every illusion is dealt through the mind. When an illusionist is a first class they can kill there enemy’s with their illusions, for example Chrome created an illusion of lava erupting and Viper(Mammon) said that if he believed it was real for one second he would have burned.
Real Illusions
When an illusionist use their illusions combined with the power of mist flame, they will create real illusions and the illusion would be experienced in reality.
During the introduction of Mukuro's First Realm, it was stated that it grants him the power to create real illusions capable of manifesting in the physical/real world. However, it wasn't until during the Future Arc that real illusions were seen.