About the Pi
The Raspberry Pi is a $25(Model A) to $35(Model B) computer, that runs on a 700MHz Arm 6 CPU. There are many Linux distrobutions that are ported to it, and some other OSes such as Risc OS. It has a composite out, 3.5mm stereo audio out, HDMI out (With audio), and on the Model A a single USB port. The Model B has 2 USB ports, and a RJ45 Ethernet port. You can use it as a tiny webserver, fileserver, XBMC media box, and many more things. Both models have GPIO (General Purpose Input Output) pins, which can be hooked up to many things. The Pi is powered by a MicroUSB cable (Like most modern Andriod Phones use), and can use most USB devices a normal computer can. It boots off of a standard SD card. Many people have used them for things such as a Commodore 64 Floppy Drive replacement, and an interface for an Apple ][ or Mac Plus to be connected to the internet.
Xbmc
One of the things I have done with the Raspberry Pi is put XBMC Media Center (Called PiBMC specifically) , and I can steam video, music, and images over the network. You can also use Youtube, WITH REWIND AND FAST FORWARD! It runs extremely well, using the built in interface. The Pi runs really well with PiBMC, and allows me to watch Youtube, steam music, and other content over the network. There is even a Firefox addon that allows you to open the youtube video on the XBMC device.