Electricity is the movement of electrons through a conductor. Electrons are usually found orbiting the nucleus of an atom. Materials that have 'free' electrons are conductors. Metals are very good conductors.
Electricity occurs naturally, in lightning, in our bodies. Electricity has been known about for long time. 150 years ago electricity became more than a curiosity through the work of people like Thomas Edison. These people worked out how to generate to usable quantities of electricity. Two different forms of electricity were developed: Alternating Current (AC) and Direct Current (DC). In AC the electrons move in one direction and then the other. In DC the electrons move continously in one direction. There was a divide about which form to use as the standard, but AC was adopted. AC became the standard because it can be transmitted with less power loss, allowing less power stations and locating them further from cities.
Electricity is first generated at a power station, then transmitted over powerlines to where it is used.
Electricity is generated when magnetic fields move through a conductor. It is only generated when the magnetic fields are changing. You can generate electricity by moving a magnet next to a wire.
Most electricity is generated in coal, gas, oil or nuclear power plants. Hydro is also used, but much less so.
All of these involve spinning a turbine. A turbine looks a bit like a propellor or fan but thicker and long. In Hydro it is water directly turning the turbine, where as the others work by the following: The fuel is combusted (burned), and the heat generated is used to boil water - creating steam. This steam rises very fast and runs through a turbine, turning it rapidly.
The spinning of the turbine is what generates the electricity. Put simply turbines contain a magnet, which is spun very fast by the steam or water. The magnetic field put out the by the magnet is thus moving very fast. Surrounding the turbine are coils of wire (conductor), which the magnetic field moves through. This induces electricity in the wires.
The amount of electricity generated depends on the speed of the turbine, the size of the magnet (and thus its magnetic field), the number and size of wire coils and a few other factors.
When electricity is generated, it is not created but rather converted from one form of energy to another. From energy 'stored' in chemicals (gas, coal) to electrical energy.
Electricity can be transmitted a long way. It is transmitted via large cables to near where it is going to be used. It is trasmitted at very high voltages, which reduces power loss (coming soon: an explanation on power, power loss and transformers). When it gets close to where it will be used it is 'stepped down' to the voltage normally found in the home (usually around 110V or 240V depending on the country).
Once it arrives at its 'destination' electricity is drawn by electrical appliances.
Solar is a bit different. See how here: Solar Basics