The Raspberry Pi is the "oh gosh, it's so cute!" little single-board computer that has captured the imagination of hobbyists and students around the world. It's not the only single-board computer available (Arduino!), and not the only one with a sizeable following, but it's cheap and incredibly flexible. The only reason I don't have one yet is that I am tight with a buck and I just upgraded my laptop to an SSD. My next project will likely be to replace my big, dusty media center PC (the guts of which are about 8 years old) with a Raspberry Pi-based system. Sweet.
If you are at all interested in this kind of thing, PC World put out a nice article on how to get started, how to load up the Raspberry Pi system and start having fun. It's very beginner-friendly, but still has some meat to it.