Electrons are part of the atoms, along with protons and neutrons. Protons and neutrons constitute the nucleus of the atom and the electrons, which are much smaller, move around the nucleus at a large distance. We can imagine the atom as a tiny solar system where the Sun is the nucleus. Since their discovery, they have been used in a variety of ways. All sorts of devices have been built to get the electrons to do something interesting. Not to mention that they are essential to the understanding of chemistry .
Electrons can be forced to move around a circuit, where they are pushed by a force. The stronger the force, the faster electrons can move . A group of electrons moving is called an electric current (I) , or a current of electrons (it is a good name, isn't?). A group of electrons not moving is called a charge, or an electrical charge (Q). The force is proportional to the voltage (V), the higher the voltage, the higher the current.
As the electrons travel along the wire, they encounter obstacles which slow them down. These can be resistances (R) for instance. Others can be a light bulb, or a buzzer, or a motor etc...Furthermore, there is a resistance caused by the wire itself, which is some sort of friction between the moving electrons and the wire. The voltage must be kept on so that the electrons are kept moving despite the obstacles.
Perhaps one of the most exciting electrical devices is the transistor, which makes possible the existence of computers, TV's, stereos and almost every single electric appliance we see nowadays. An appliance like a TV is a complex combination of transistors, resistances, capacitors and many other components. The current of electrons can do so many things ... This "type" of electricity , which powers devices, motors and can travel in power lines or in small wires around the home is what is seen as "Normal" electricity" (as opposed to static electricity).