In certain years, an extra month of Adar is added to the Jewish calendar. The reason for this occasional extension of the year is to synchronize the Jewish calendar with the solar calendar. The solar calendar, which is used by the Christian world, is based upon the earth's revolution around the sun, which occurs over the course of 365 days. The Jewish calendar, by contrast, is arranged on the basis of the moon's revolution around the earth, which occurs approximately every 28-29 days. The Jewish year is determined by twelve revolutions of the moon, which spans 354 days. Hence, the Jewish calendar is eleven days shorter than the solar calendar. If we would follow only the lunar system, all our holidays would fall each year eleven days earlier than the previous year, and they could thus fall during any season. (In fact, the Moslems' calendar follows exclusively the lunar system, and so their holidays can fall at any time during the year.) The Torah requires that Pesach always be observed during the spring season, and it is therefore necessary to adjust the lunar calendar so it is synchronized with the solar calendar, assuring that each Jewish holiday falls in its appropriate season. We do this by adding a month every several years. The month that is added is a second month of Adar. (Interestingly enough, the zodiacal sign of the month of Adar is Pisces, which has two distinct images, corresponding to the two months of Adar. The sign of every other month has only one image.)
During a leap year, when an extra Adar is added, the second Adar is considered the actual month of Adar, and the first Adar is regarded as the additional month. Therefore, we celebrate Purim during the second Adar, and we likewise observe Shabbat Shekalim and Shabbat Zachor during that month.
If a child was born in Adar Sheni (the second Adar) during a leap year, and the year of his Bar-Misva is also a leap year, then, quite obviously, he becomes a Bar-Misva on his birthday in Adar Sheni. And a boy born during Adar Rishon (the first Adar) during a leap year becomes Bar-Misva in Adar Rishon if that year is a leap year.
If a child was born in Adar Rishon during a leap year, and the year of his Bar-Misva is a regular year, then he becomes Bar-Misva on his birthday during the month of Adar. One might have thought that we should consider Adar Rishon the equivalent of Shevat – the month before Adar – such that his Bar-Misva should occur in Shevat. This is not the case, as Halacha considers this boy to have been born during Adar, and so be becomes a Bar-Misva in Adar. Conversely, if a boy was born in Nissan during a regular year, and the year of his Bar-Misva is a leap year, he becomes a Bar-Misva during Nissan. We do not consider his birthday to be in Adar Sheni – the month after the first Adar – but rather in Nissan.
These Halachot result in an intriguing anomaly – that a boy can become Bar-Misva before a boy who is older than him. If a boy was born toward the end of Adar Rishon in a leap year, and another boy was born several days later, toward the beginning of Adar Sheni, then if the year of their Bar-Misva is a regular year, the younger boy will celebrate his Bar-Misva first. Since he was born in the beginning of Adar Sheni, he will become Bar-Misva on that date in Adar, whereas the older boy – who was born at the end of Adar Rishon – will not become Bar-Misva until that date arrives toward the end of Adar.