The Raspberry Pi is the main component of all examples on this website. It contains an ARM processor which does all of the computation, and a wide variety of input and output ports to allow it to communicate with the outside world.
Raspberry Pis are available for purchase online from two distributors: Premier Farnell and RS Components. They trade under different names depending on where in the world you are, so see here for direct links. It is also available as part of a larger kit from Maplin.