If you are not familiar with the Raspberry PI, it is basically a full computer on a single board. The current version (v3) has bluetooth, Wifi, USB, HDMI output for a monitor, audio and more--all for $35! It runs Linux as the operating system (which is free). It includes 40 GPIO ports on the board. GPIO are awesome (here's how) since they are FAST can be used for anything. Some hams figured out a way to modulate the digital signal on a couple of GPIOs in way that it generates an RF signal. Plug a tuned wire into it like an antenna and PROOF...you've got a transmitter.
One problem is that since it is a down and dirty adaptation, it produces lots of harmonics and outputs about 10mW. The TAPR folks created a new board that plugs into the GPIO, adding band-pass filtering and cleans up the signal. Another guy in the UK did something similar but also added an amplifier boosting the signal to 150mW. And the UK version is actually cheaper than the TAPR one.
So, what can you do with it?? Well, plug SDR stick into it and you could use it as a QRP rig. But many folks are using it as a WSPR rig (pronounced "whisper" and stands for "Weak Signal Propagation Reporter"). WSPRnet.org is a group of people who use the same (free) software to control low-power beacons all around the world. The radio transmits a digital message then listens and logs all the stations it hears. It automatically uploads the data to the website which compiles a comprehensive, real-time picture of world-wide propagation.
Other Interesting Sites:
http://www.rtl-sdr.com/building-a-ham-tranceiver-with-an-rtl-sdr-raspberry-pi-and-rpitx/
http://www.rtl-sdr.com/transmitting-fm-am-ssb-sstv-and-fsq-with-just-a-raspberry-pi/
https://www.youtube.com/watch?v=6smyUoLugsg
http://hackaday.com/2014/06/15/easily-turn-your-raspberry-pi-into-an-fm-transmitter/