Power plant turbine/alternator sets do run at a constant speed, so that we get a constant frequency of AC (60 Hz around here).
However, let's say you switch your light bulb from a 60W incandescent to a, say, 12W fluorescent (giving the equivalent light output). Now, you've just reduced your power consumption by 48W. The power company does indeed have regulators to keep your line voltage (more or less) stable, so your current consumption goes down.
That reduced power/current consumption now ripples back up the distribution system all the way to that ultra-monster turbine/alternator. Due to voltage regulators and steam throttles and boiler thermostats and oil pump regulators and such, the horsepower being delivered to the alternator goes from 100,000 horsepower to 99,999.98 horsepower. The oil flow to the boiler's burner goes from 50,000 gallons per day to 49,999.998 gallons per day. (I made that oil number up.)
Bear in mind, this all happened because you unscrewed your incandescent bulb and screwed in a fluorescent one.
Now, people in your area duplicate your action by 60,000 times. Now the power plant has decreased its oil consumption 60,000 x .002, or 120 gallons, per day.
And, of course, a similar effect obtains for power plants using other energy sources.
One final comment. 120 gallons of oil savings per day at the power plant looks like a drop in the bucket, so to speak, for all that Green light-bulb-switchin' goin' on. But remember that I made up those oil numbers, so the savings might be more significant than that. Or maybe less. < ]B^)
They want you to hitchike around in sandals, filthy clothes and long hair. Just like them.