In the early 1900s, rabbinic authorities had to determine exactly what electricity was from an halachic (Jewish legal) perspective. The first uses of electricity were, of course, for light and heat. And just as one is permitted to have a fire lit before Shabbat remain lit throughout Shabbat, it was determined that one may leave electric lights on throughout Shabbat. As scientists and inventors began to find other ways of using electricity, such as fans and radios which produce neither light nor heat, the question of electricity’s permissibility on Shabbat resurfaced.
The halachic ramifications of electricity and electric appliances will, perhaps, be a debate that continues until a completely different source of energy has been discovered. Until that time, however, there are several m’lachot which may be being violated by the use of electric devices on Shabbat:
1) Nolad (lit. birthing): The rabbinic prohibition against creating something new on Shabbat.
2) Boneh (building): The m’la’cha of building would include the act of completing the circuit, of building an electrical bridge when one turns on an appliance or light.
3) Makeh B’patish (final hammer blow): Similar to boneh, this m’la’cha is violated when a circuit is completed, thus finishing the "job."
One wishing to guard Shabbat by avoiding the 39 m'lach'ot would, therefore, need to refrain from turning on, turning off or altering (such as changing the volume) any electrical item.
There are many ways that technology has altered how electricity can be used on Shabbat. Many households use preset timers to control household lights. This is permitted because the action was set in motion before Shabbat began. In recent years, Shabbat observant engineers have worked with large appliance manufacturers to create "Shabbat friendly" ovens, refrigerators and even dishwashers.