The regulator gene produces repressor, inactivated in the presence of inducer, that is lactose, RNA polymerase then gets access to the promoter gene and transcription proceeds
z gene codes for beta-galactosidase (ß-gal), responsible for the hydrolysis of the disaccharide lactose into galactose and glucose
y gene codes for permease, which increases permeability of the cell to ßgalactosides / lactose
a gene encodes enzyme transacetylase