Irregular astigmatism is by definition any astigmatism not correctable with a spectacle lens. [This assumes the spectacle lens is spherocylindrical which almost always the case.] It is usually caused by asymmetrical irregularities of the corneal surface.
A contact lens, however, seated on the eye over the cornea, can often work to smooth over these irregularities because the space behind the contact lens and the corneal surface below is filled with tears. This makes the contact lens’ smooth and regular surface into the new “refracting” or focusing interface with the air.