This article is from the Calendars FAQ, by Claus Tondering email@example.com with numerous contributions by others.
The Romans didn't number the days sequentially from 1. Instead they
had three fixed points in each month:
"Kalendae" (or "Calendae"), which was the first day of the month.
"Idus", which was the 13th day of January, February, April,
June, August, September, November, and December, or
the 15th day of March, May, July, or October.
"Nonae", which was the 9th day before Idus (counting Idus
itself as the 1st day).
The days between Kalendae and Nonae were called "the 5th day before
Nonae", "the 4th day before Nonae", "the 3rd day before Nonae", and
"the day before Nonae". (There was no "2nd day before Nonae". This was
because of the inclusive way of counting used by the Romans: To them,
Nonae itself was the first day, and thus "the 2nd day before" and "the
day before" would mean the same thing.)
Similarly, the days between Nonae and Idus were called "the Xth day
before Idus", and the days after Idus were called "the Xth day before
Kalendae (of the next month)".
Julius Caesar decreed that in leap years the "6th day before Kalendae
of March" should be doubled. So in contrast to our present system, in
which we introduce an extra date (29 February), the Romans had the
same date twice in leap years. The doubling of the 6th day before
Kalendae of March is the origin of the word "bissextile". If we
create a list of equivalences between the Roman days and our current
days of February in a leap year, we get the following:
7th day before Kalendae of March 23 February 6th day before Kalendae of March 24 February 6th day before Kalendae of March 25 February 5th day before Kalendae of March 26 February 4th day before Kalendae of March 27 February 3rd day before Kalendae of March 28 February the day before Kalendae of March 29 February Kalendae of March 1 March