What's the deal with two Adars?

(1) Observe the month of Aviv, and keep Pesach unto the LORD your God; for in the month of Aviv the LORD your God brought you forth out of Egypt by night.

(1) A leap year is a year in which another month has been added. And we only ever add an Adar and make two Adars, an Adar Rishon (first Adar) and an Adar Sheini (Second Adar). And why do we add this month? Because of the spring time, so that the Passover will fall at that time, as it is said (Deuteronomy 16:1) "Guard the month of the spring", that this month should be in the spring. And if it wasn't for the addition of this month, Passover would sometimes come in the days of the sun (the summer) and sometimes in the days of the rain (the winter).

(1) שמור את חודש האביב, make sure that the month of Nissan always occurs in the spring, by manipulating the calendar, if necessary and inserting an extra month of Adar. By doing this the solar orbit (year) and the lunar orbits, (12 moons equaling a year) can be brought into line with each other.

(20) And Mordechai wrote these things, and sent letters to all the Jews that were in all the provinces of the king Achashverosh, both near and far, (21) to enjoin them that they should keep the fourteenth day of the month Adar, and the fifteenth day of the same, yearly, (22) the days wherein the Jews had rest from their enemies, and the month which was turned unto them from sorrow to gladness, and from mourning into a good day; that they should make them days of feasting and gladness, and of sending portions one to another, and gifts to the poor.

During a leap year, the 14th and 15th days of Adar Rishon, even though we don’t read the Megilla on them, nevertheless it is forbidden to give a eulogy or fast, and we don’t say Tachanun, and we don’t say Lamnatzeach. It is good to behave a little happier than usual and feast a little, on the 14th for the villages (outside of the walled cities), and on the 15th for the walled cities. And we don’t read the Megilla during Adar Rishon, like it says in מגילת אסתר ט כא, that is referring to the Adar that is next to Nissan, but during a leap year, we don’t celebrate Purim other than during the Adar that is next to Nissan. This is because we want to put redemption with redemption, that is Purim and Pesach, it is good.

And [this] is not lucid; as behold, we say in the gemara, "Concerning the matter of eulogies and fasts, this and that (both months) are the same." [From this] it is implied that feasting and joy are not [treated the same in both months]. As per force, one is not dependent upon the other; as if one were dependent upon the other, let [the gemara] make us understand that feasting and joy are practiced on [the fourteenth and fifteenth of the first Adar], and automatically, it would be forbidden for eulogies. As behold, the days that are mentioned in Megillat Taanit that are forbidden for eulogies [also] do not have feasting and joy (so we see that feasting implies not having eulogies, even if having no eulogies does not imply feasting). And so is the law (halakha), that there is no need to be stringent to make feasting and joy in the first Adar.

(1) The day of the 14th and the 15th of the First month of Adar [in a leap year] we do not fall upon our faces [recite tachanun] and we do not say (the Psalm) a song - Hashem will answer you on a day of suffering, and on them [the 14th and 15th of Adar I] it is forbidden to eulogize or fast. There are those who say that even eulogies and fasting is permitted. Rema: the practice is according to the first understanding. There are those who say that one is obligated to increase in joy and feasting on the 14th of Adar I however this is not the practice. Nonetheless one should increase slightly their joy and feasting in order to fulfill the words of those who are stringent 'But he that is of a merry heart hath a continual feast (Proverbs 15:15).'

(4) If the Megillah was read in first of Adar, and the year was [subsequently] intercalated (a leap year was declared), we read it in second of Adar. There is no difference between the first Adar and the second Adar except the reading of the Megillah and gifts to the poor.