The large module is the the XL6009 Boost Converter, which is boosting a 5 V source to 21 V. There is a small screw on it that you can turn to select other voltages (i think it goes up to 35 V).
It is tied into an NPN transistor, set up for switching. The base of the switch is driven by a 5 V signal from the Uno, with a 10k resistor, which turns on the collector-emitter path, which being driven by the 21 V source, with a 1k resistor, and providing current for the LED.
I needed a 21 V source for my EPROM programming project, but needed it to be controlled by a 5 V AVR pin.
A pack of XL6009 Boost Converters is available for about $12 from Amazon.
The Libre Hacker 
Great setup!
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