Capacitors store energy, their ability to store energy is called capacitance and is measured in farads which is abbreviated to F (although 1 farad is a huge amount of energy).
Capacitors charge rapidly and can discharge even quicker. This is why they are used when an application may need to suddenly draw a large amount of current. They are also used to smooth signals in a similar way to how a spring works in car suspension. If an electrical signal goes from a low voltage to a high voltage and its attached to a capacitor, the capacitor will have to charge before the signal can increase fully. There is a similar effect when the voltage is dropping as the capacitor will discharge, applying more current to the circuit and keeping the voltage high. This is why capacitors are used to smooth signals and filter out noise.
Many signalling applications require accurate choice of capacitor, but for simple circuits the choice is less critical, just remember the higher the better. Capacitors are usually put between the supply and ground of a digital circuit, this is to smooth the voltage supply and provide on demand current for the rapid switching of digital circuits.
Electrolytic (Polarised) Capacitors
Electrolytic capacitors must always have the voltage applied the correct way around. They have one lead longer than the other, this is the positive lead. The negative lead is usually also marked on the body of the capacitor.
Electrolytic capacitors are used because they typically have a larger capacitance than standard capacitors.
for much more information than you will ever need, see the wikipedia page
1farad = 1F
1F = 1000mF
1mF = 1000µF
1µF = 1000nF
1nF = 1000pF