This fascinating TED Talk given by Tim Post talks about lucid dream research as well as what lucid dreaming is. Tim does a great job at clearly explaining what lucid dreaming is, the lucid dream research that has been done, as well as how to induce a lucid dream. Watching this video will be time well spent!
If you are interested in lucid dream research, you may also want to check out How To Lucid Dream, Is Lucid Dreaming Dangerous, or Why Would You Want to Lucid Dream.