Now, under normal conditions, when glucose is plentiful and lactose is scarce, E Coli doesn’t  want to transcribe the lac gene. In this situation, a protein called the lac repressor sits on the DNA, bound to the operator. Polymerase can’t transcribe the gene; it’s blocked by the repressor. So no lac genes can be expressed.

Now, let’s say you’re E Coli, and a couple of French guys come along and put you on a lactose diet. All of a suddden, you need to make those lac genes into protein, so you can chew lactose. No problem. There’s a special site on the lac repressor where lactose can bind. When lactose binds the repressor, it falls off the operator. Now polymerase is free to transcribe the genes into protein, and your lactose diet becomes digestible.

That’s not the whole picture, though. Consider—out in “the wild”, you E. Coli types encounter situations where both lactose and glucose are available. You prefer glucose, and will continue to eat that preferentially. Still, variety is the spice of life. So in these situations you don’t want your lac genes turned all the way off, but you don’t want them screaming, either. As it happens, when the repressor falls off in the presence of both lactose and glucose, the amount of lac gene actually transcribed is only fair to middlin’.

But when the glucose is all used up, or when the French guys take it away, you really need to crank up the lac expression. In the absence of glucose, E Coli makes a lot of a little molecule called cyclic AMP, or cAMP. cAMP binds to a protein called CAP, which stands for catabolite activator protein. When  cAMP binds to CAP (that is, when glucose is low), it causes CAP to bind to the upstream part of the promotor on the lac operon. And that causes increased transcription, because CAP makes it easier and faster for polymerase to bind the exact part of the promotor it needs to take off.
 

Figure 23. The lac operon. Animated sequence. Be patient--what, you got a hot date?