Mayans lived in countries now known as Honduras and Guatemala in central America around 2000 years ago. They had a calendar that was much more complicated than ours but one think was grouping periods of 125 years together. December 2012 is the end of 5 of these 125 year periods so some people believe that this means the world will end. Scientists do not believe there is any evidence for this superstition, and no evidence that 21st December 2012 will be any worse or better than any other day.
It’s a really popular idea though and a couple of movies have been made about it. There have been lots of people who have predicted that the world would end on certain dates which haven’t come true.
Katherine makes a good point and I think it is something that has grown more popular as Hollywood could make some exciting action films on it without much thought so it made more people aware however it’s not something you should be worried about 🙂