Much connected load is constant impedance in nature (hot water tanks, space heaters, light bulbs, etc).
When you reduce supply voltages, you reduce the current through these impedances (Ohm's law, V=IR)
Therefore, you reduce the Power as well (P=IV)
Some of these loads will simply run longer to consume roughly the same amount of energy, as the water in the heater will still need to reach a setpoint before the tank turns off, but will use less peak power while doing so.
Some of these loads, like the light bulbs, will simply not be as bright while they are on, saving both energy and peak power.
So, voltage reduction DOES result in slightly less energy consumption, but more properly is used to reduce peak POWER by speading out the energy use over more time.
Care must be taken to ensure that these reduced voltages are not so low that equipment gets damaged as a result.