Structural genes in Lac-operon are switched off when
Operator genes contain the codes that are necessary to begin the process of transcribing DNA into mRNA. Operator and repressor together controls the switching on & off of the operon; when repressor is bound with operator it will not allow the RNA polymerase to transcribe the structural gene. On the other hand when the repressor is not bound with the operator, it will allow RNA polymerase to kick off the process of transcription.
Inducers are the molecules which bind with the repressor that leads to the conformational change in the structure of the repressor protein thus not allowing the repressor protein to bind the operator.
Allolactose binds to the Lac repressor and makes it change shape so it can no longer bind DNA. Allolactose is an example of an inducer, a small molecule that triggers expression of a gene or operon.