This upcoming Sabbath is the first day of the first Adar, which will be followed one month later by Adar II. On standard years, there is only one month of Adar, but in order to maintain Nisan as a spring month, an additional Adar month is added on 7 times in 10 years. We celebrate the holiday of Purim in the second Adar, so that it remains 30 days before the holiday of Pesach [Passover]. That may indicate that we regard the second Adar as the "real" one, but that is not so cut-and-dried.
This question was addressed in http://divreichaim.blogspot.com/2008/02/double-adar-and-yahrzeit-of-moshe.html:
I posted the safeik of the Yerushalmi whether which month, Adar I or Adar II, is the “real” and which is the addition. There is more to be said on the halachic issue, but for today I want to focus on what the debate might teach us for our avodas Hashem. The Shem m’Shmuel writes that the number 12 is symbolic of the natural order, teva; e.g. 12 constellations in the sky, 12 months in a regular year, 12 hours in a halachic day. The number 13 is symbolic of transcending the natural order; e.g. 13 middos harachamim are used to ask G-d to extend his mercy beyond what we deserve. There is something to be said for living within natural boundaries – go to work, have a regular seder in learning, take care of chores around the house, repeat. This is the world of the number 12. But sometimes a person needs to make a jump into the world of 13, a world without limits or boundaries, a world where a person can be inspired by ideas that transcend the practical routine even while knowing that the world of 12 will ultimately pull one back to reality. The world of 13 provides the boost, the vision, without which a person could not sustain himself day after day in the world of 12. So which is the ikkar [main thing] and which is the tafeil, [subordinate part] which is the “real” world and which is the “tosefes” [added element]? The world of 13 is inspiring, but unless it impacts the day to day world of 12, its platitudes are meaningless. On the other hand, the world of 12 has no meaning without the goal and vision of the world of 13 to sustain it. Which Adar is the “real” Adar – the 12th month, or the 13th?
Though we think of the zodiac as corresponding to the 12 months, scientists actually identify 13 constellations in the earth's orbit around the sun (see strdu.com/constellations.html). The signs of the zodiac correspond to the 12 months of the year, but the additional constellation matches up to the number 13. Those number match up with the variations in the lunar calendar and to the number of the tribes of Israel. Though they are traditionally regarded as 12, when the tribe of Levi is added, the number comes out to 13.
Related articles credit to the women