A repressor is a regulatory protein that binds to DNA at the operator and will not allow RNA polymerase to transcribe genes. Therefore, the genes can be transcribed. So, the genes are automatically turned on in the presence of lactose. Binding to repressor is non-covalent, so it is reversible. Lactose is then called the inducer.
Operons can also be repressible operons.
This is called repressible because the addition of the relevant molecule causes repression. In general, degradative pathways are inducible and synthetic pathways are repressible. Both inducible and repressible mechanisms are examples of negative control of transcription, because the repressor can only turn genes off. Yes, and it exists in the lac operon. RNA polymerase can bind the promoter, but not very well.