The "13th sign" is Ophiuchus, in which the sun appears from November 30 to December 17. The traditional solar zodiac of 12 sun signs of equal length originated with the Babylonians and was adopted by the Greeks. Ophiuchus was not a part of the Babylonian zodiac, and the Greeks retained the 12-sign zodiac even though their own sky maps indicated that the sun's annual path did indeed pass through Ophiuchus.

http://www.geocities.com/astrologyconstellations/ophiuchus.htm
http://www.geocities.com/astrologyprinciples/zodiacwheel.htm

There was never an official 13th sign of the zodiac in ancient times. A modern "real solar zodiac" has been devised but is not in widespread use.

http://www.geocities.com/astrologyzodiacs/realsolarzodiac.htm

This zodiac is based on the modern boundaries of the constellations, which were not defined until 1930 and which do not necessarily correspond to the constellations' "traditional" borders.

http://www.iau.org/public_press/themes/constellations/

Actually there are 13 constellations that the sun passes through. Ophiucus, the Serpent Bearer, is ignored by astrology. It makes up a little over half a month. Ignoring Ophiucus only serves to make astrology more inaccurate (is that possible?).

Here's what Wikipedia says about the thirteenth sign of the zodiac.

"Although Ophiuchus intersects the ecliptic, it is not a zodiacal sign in most versions of astrology. The signs are defined as 30-degree segments of the ecliptic, of which there are twelve, and they are named after nearby constellations at the time the system was developed, rather than being defined by the modern constellations. However, a few sidereal astrologers consider the Sun to be in the sign Ophiuchus when it is in the constellation Ophiuchus, which as of 2008 is November 30 to December 17."

"Although not incorporated into the 12-sign zodiac, Ophiuchus and some of the fixed stars in it were sometimes used by astrologers in antiquity as extra-zodiacal indicators (i.e. astrologically significant celestial phenomena lying outside of the 12-sign zodiac proper). An anonymous 4th century astrologer, often known as Anonymous of 379, seems to have associated "the bright star of Ophiuchus", likely α Ophiuchi, with doctors, healers or physicians (ἰατρῶν)."

Basically the sun passes through it, but mainstream astrology doesn't recognize it as a true zodiac sign, because the sun only passes through it for 19 or so days.

Following the Wikipedia link to Sidereal Astrology you can learn about the differences between Tropical and Sidereal Astrology.

There isn't a 13 month, but the 13th sign is Ophiucus 11-30-12-17. The 13 signs divide up the 12 months of the year.
http://www.geocities.com/astrologyconstellations/ophiuchus.htm

Ophiuchus the 13th sign of the Zodiac - also known as Serpentarius, the Serpent Holder.

The constellation Ophiuchus has been known about since ancient times, but you wouldn’t know it.
It was never added to the Zodiac chart as astrologers said that the Sun went straight from Scorpius into Sagittarius, disregarding the fact that the sun travelled through Ophiuchus for 19 days before entering Sagittarius.

Basically then what that means is that there is another sign! a lost sign.

Ophiuchus - The 13th Sign of the Zodiac:
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The 13th sign of the zodiac, unlike the other 12 signs is actually associated with a real person. In the 27th Century BCE in Ancient Egypt lived a man known as Imhotep. Imhotep was known as ‘Aesclepius’ by the Ancient Greeks, however the attributes are the same under either name.

Serpent holder

One of Imhoteps abilities was healing and it is said that it was he who introduced it to mankind. His accomplishments also included a wide knowledge of medicine. The serpent or snake symbol which is still used today to symbolize the medical profession was also used to represent Imhotep. Below is a list of attributes associated with the Serpent Holder, Imhotep i.e Aesclepius. The descriptions below are associated with the 13th sign - Ophiuchus.

Imhotep

Many people are envious of this subject as he progresses well throughout life.
A seeker of wisdom and knowledge
Many people are jealous of this person
Tends to go for the more flamboyant in dress sense, favouring bright colours.
Authority looks upon him well.
Would make a great architect or builder.
Number 12 is this persons lucky number.
This person will have a big family but leave home at an early age.

OPHIUCHUS = NOVEMBER 30 - DECEMBER 17