There is little to be said about this circuit. All the work is done by the regulator. The 7809 can deliver up to 2 amps continuous output whilst maintaining a low noise and very well regulated supply. The circuit will work without the extra components, but for reverse polarity protection a 1N5400 diode (D1) is provided at the input, extra smoothing being provided by C1. The output stage includes C2 for extra filtering, if powering a logic circuit than a 100nF (C3) capacitor is also desirable to remove any high frequency switching noise.
circuit from http://www.extremecircuits.net/2010/03/9-volt-2-ampere-dc-regulated-power.html