This article is from the alt.usage.english FAQ, by Mark Israel firstname.lastname@example.org with numerous contributions by others.
Many of us will be happy if people can even spell "millennium"!
As Mark Brader has noted in the relevant entry in the
news.announce.newusers FAQ "Answers to Frequently Asked Questions
about Usenet", the A.D. calendar system was devised before
"origin 0 counting" was invented. The first year assumed
(incorrectly, as most scholars now believe) to have begun after
Jesus' birth was A.D. 1, not A.D. 0; the previous year was 1 B.C.
This gives us the millennia 1-1000, 1001-2000, and 2001-3000. On
the other hand, the convenience of grouping together years,
decades, and centuries having like digits is obvious. The standard
joke is that those who say the next millennium will begin in 2001
and not 2000 are right, but they'll be missing one hell of a party!