Updated: The New York Times has an incredibly illustrative infographic about how a meltdown occurs, and how a reactor shuts down. It's a must see.
Original post: As the situation at the Fukushima district nuclear power plants in Japan has escalated from issue to emergency, a lot of people have been asking for a basic explanation of what exactly a meltdown is. This Reuters video—specific to the Fukushima plant—was the best, most clear and simple description that I could find.