Electricity is the flow or presence of electric charge. Electricity provides the power for electric apparatus, for instance, televisions, computers, microwave ovens, and more generally anything that needs to be plugged in to work. Electric energy is electric power multiplied by the time period that the power is provided. Electric energy can be stored in batteries, which are used in portable devices such as flashlights and walkmans. A battery runs out of energy after we used much power during a short period, or little power during a long period. Electricity is also the cause of lightning: electric charges going through the air cause the air to give off light flashes. Another phenomenon caused by electricity, called static electricity, is that by rubbing a balloon against a sweater electric charge is transferred to the balloon. When you hold the charged balloon close to your hair, the balloon will attract your hair by electric forces.
In a flashlight, the batteries produce an electric current that is transported to a light bulb. The current provides the power for the light bulb to produce light, and is then transported back to the battery. The loop formed by the battery, the light bulb, and the connections between them is an electric circuit. This needs to be a closed loop; if one of the connections is broken or the light bulb is removed, then no current will run. Whenever we want to extract energy from electricity we need a closed loop.
A power plant produces electricity. Electrical transformers transform this into a high-voltage, low-current electricity for more efficient long-distance transport. The power loss in this transport is proportional to the strength of the current and therefore low-current high-voltage electricity is more efficient (gives less power loss) than high-current low-voltage. High voltage cables transport this electricity over miles to houses and factories. Additional transformers reduce this to a much lower voltage (120 volts in North America and 240 volts in Europe) for safety, eventually bringing it to the electricity sockets in your house.
Batteries produce an electric current which always flows in one direction, which is called direct current (DC). No good method for changing voltages of direct current existed in the nineteenth century, so direct current power plants had to be located within a few miles of consumers. An alternative approach, alternating current (AC), has electric voltage switching many times per second. Voltages of alternating current can be increased and decreased easily with transformers, so alternating currents can be carried long distances with high voltage and low power loss, which is why AC won out over DC.
If you plug in the television, then an electric current can run through the cable to the television, providing the power which it needs. The current returns through a different wire in the same cable to the socket, thus closing the circuit. An electricity plug thus has at least two pins, one for bringing the current from the socket to the television and the other one for returning it.
Electric current is caused by the movement of electrons, very small particles with a negative elementary charge that appear in all materials. In some materials, like wood and plastics, the electrons stick to their place and thus electric current cannot run through these materials or only with great difficulties. Such materials have a high resistance and are called insulators. Conductors are materials, like copper and many other metals, in which the electrons can move around relatively freely; they can carry a current. Semiconductors can act either as conductors or as insulators depending on circumstance.
Electricity is closely related to magnetism. Maxwell's equations mathematically describe both phenomena. Physicists usually study both phenomena together, and they call the combination electromagnetism. Electromagnetism is one of the four fundamental forces (the others are gravity, the weak force and the strong force). See the article on the Standard Model.