Function
Capacitors store electric charge. They are used with resistors in timing circuits because it takes time for a capacitor to fill with charge. They are used to smooth varying DC supplies by acting as a reservoir of charge. They are also used in filter circuits because capacitors easily pass AC (changing) signals but they block DC (constant) signals.
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Capacitance
This is a measure of a capacitor's ability to store charge. A large capacitance means that more charge can be stored. Capacitance is measured in farads, symbol F. However 1F is very large, so prefixes are used to show the smaller values.
Three prefixes (multipliers) are used, µ (micro), n (nano) and p (pico):

µ means 10-6 (millionth), so 1000000µF = 1F
n means 10-9 (thousand-millionth), so 1000nF = 1µF
p means 10-12 (million-millionth), so 1000pF = 1nF
Capacitor values can be very difficult to find because there are many types of capacitor with different labelling systems!

Examples:

Circuit symbol:

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