If there is no lactose present in the environment, the following series of events occurs:

The lac I gene is transcribed (remember, it is expressed constitutively), and the mRNA is translated, producing the lac repressor. The repressor binds to the operator, and blocks RNA polymerase. With RNA polymerase blocked, there is no transcription, and the enzymes for lactose metabolism are not synthesized. This is good, because there is no lactose to metabolize.

When Lactose is Present

If there is lactose in the environment, the events unfold differently. A small amount of the lactose gets into the cell, and affects regulation of the operon:

The lac repressor is still synthesized. As mentioned previously, the repressor can bind to lactose. When it does so, the repressor undergoes a conformational change (change of shape). Molecules that change shape when they bind to another molecule are called allosteric molecules. When it undergoes the conformational change, the lac repressor is unable to bind to the operator region. RNA polymerase is therefore not blocked, and is able to transcribe the genes of the operon. The enzymes encoded by those genes will be produced, the lac permease will transport more lactose into the cell, and beta-galactosidase will cleave the lactose into glucose and galactose, which can then be further metabolized by other enzymes, producing energy for the cell. Lactose, therefore, is able to induce the synthesis of the enzymes necessary for its metabolism (by preventing the action of the repressor). As such, lactose is the inducer of the lac operon.

The bottom line for the lac operon, then, is that when lactose is absent, lactose-metabolizing enzymes are not produced, and when lactose is present, those enzymes are produced.