Economy Seven is a general term for a type of electrical energy billing plan that has night-time 'off-peak' rates and either has rate penalty for use during the day or (in extreme cases) lives on a separate circuit that is only available during the night-time hours. For more information see the excellently detailed British Residential Electric Wiring. In the UK, where (I believe) Economy Seven originated, those systems would be on between midnight and seven A.M., seven hours a day.
Why do this? The plan was originally put forth to improve energy conservation. Most industrial-sized power generation stations operate twenty-four hours a day, but demand drops off significantly during the night (when folks are asleep and not using all them gadgets). They operate 24/7 because most generating solutions require more than a few hours to start or stop completely - nuclear power, coal-burning plants, essentially anything with a steam turbine will require hours of startup. So there's all this electricity 'going to waste' during the night. This is also why electric cars make more sense than simply for their higher efficiency - in most locations, there is in fact surplus electricity going unused at night which could be used to charge the cars. It is almost impossible to store usable amounts of this power centrally; Economy Seven was an attempt to store it locally.
At the core of it, Economy Seven was usually used with home heating devices called storage heaters. During the night, cheap Economy Seven power was used to electrically heat the hot water tanks in the storage heaters which was drawn down during the day to heat the home and provide hot water. I'm unsure of the present status of Economy Seven; I have heard anecdotally from various friends in the U.K. that some places still offer it. Some offer 'Economy Ten', which is Economy Seven with the addition of three hours of off-rate use during the afternoon to 'top up' the storage heater for when folks get home. The rate is slightly higher.
Note that as homes have become more dependent on electricity, other uses of Economy Seven have arisen. For example, home appliances whose use isn't time-critical can either be wired to Economy Seven circuits or metered for Economy Seven and run with timers at night - dishwashers, clothes washers, clothes dryers - and that power draw will benefit from cheaper rates.
iamkaym notes that France also offered an equivalent of Economy Seven, complete with stored hot water!
zoeb has, I find, reviewed an album titled Domestic Economy 7, as well.