A
millennium is a period of one thousand consecutive
years. When dating years, millennia are usually taken to begin in the years divisible by one thousand, or alternatively in the year after that, e.g., 2000 or 2001. The use of the odd year came from the
Anno Domini system of religious dating, where the year 1 was supposedly the first "year of our lord" and thus the first millennium would be years 1 to 1000 and the second millennium would start in 1001.
Wikipedia has a page for each millennium: Millennia.