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1) [line 2] SHE'KALU LO CHADASHAV - its term of pregnancy was completed; the complete term of pregnancy for a Behemah Dakah (sheep and goats) is 5 months and for a Behemah Gasah (cattle), 9 months (Bechoros 8a)

2) [line 3] IBURIN
(a) A Shanah Me'uberes (a leap year) is one in which an extra month is added. The only month that is ever added is Adar, such that in a Shanah Me'uberes there are two months of Adar. The reason for adding the extra month is in order to be certain that Pesach falls in the season of Aviv (spring), as it states in the verse, "Shamor Es Chodesh ha'Aviv, v'Asisa Pesach..." - "Observe the month of Aviv, and do the Pesach Sacrifice..." (Devarim 16:1).
(b) A Beis Din of the Chachamim decides whether there is a need for a Shanah Me'uberes based upon three signs: the spring equinox; the spring season in the districts of Yehudah, Ever ha'Yarden and Galil; the ripening of fruits. 1. If, according to the calculation of the Chachamim, the spring equinox will fall on the 16th of Nisan or later, the extra month is added. The month that would have been Nisan is called Adar Sheni. 2., 3. These two signs are interrelated. If the Chachamim decide that the spring season has not come, i.e. the days are still short and dark and the fruits that are normally ripe at the time of Pesach will not have ripened, the extra month is added, even if the equinox falls before the 16th of Nisan. If spring arrived in two out of three of the districts mentioned above, the extra month was not added.
(c) Besides the principal signs mentioned above, the Chachamim list four more reasons to add an extra month, based upon necessity. 1. If the roads are impassable and will prevent the Diaspora Jews from getting to the Beis ha'Mikdash in time for the Pesach sacrifice. 2. If bridges are washed out and the journey is impossible or dangerous for the Diaspora Jews. 3. If the Diaspora Jews have started their journey, but will not arrive in Yerushalayim on time. 4. If the ovens that were meant to be used for roasting the Pesach sacrifices in Yerushalayim were destroyed during the rainy season, and there are no other substitutes for them (RAMBAM Hilchos Kidush ha'Chodesh 4:1-5).

3) [line 3] TERUMAS SHEKALIM
(a) In the Beis ha'Mikdash, many public sacrifices were offered (for example the daily Temidim, the Korbenos Musaf of Rosh Chodesh and the festivals, etc.). In order to finance these Korbanos, one half a Shekel was collected from every Jew, both those living in Eretz Yisrael and in the Golah, once a year.
(b) The half Shekalim were collected before Rosh Chodesh Nisan so that the Korbanos of the new year (which starts with the month of Nisan) would be offered from the money that was collected for the new year. On the first of Adar, Beis Din announced that the Shekalim should be collected, in order to ensure that all of the Shekalim would be collected before Rosh Chodesh Nisan (see Insights to Shekalim 2a). Some commentaries contend that a portion of the Shekalim would not arrive until after Rosh Chodesh Nisan, while others claim that all of the Shekalim arrived by Rosh Chodesh Nisan, since the Shekalim were collected from the regions further from Yerushalayim earlier in the year. (This latter opinion appears to be the conclusion of the Yerushalmi, Shekalim 2a - see Mishnas Eliyahu ibid. 2b.)
(c) The amount that was collected from each Jew was not fixed at half a Shekel. Rather, the amount given was always half of the "Matbe'a ha'Yotzei" (the primary coin in use at the time), provided that it was not *less* than the value of half a Shekel.
(d) The word "Shekel," as used in the phrase "Machatzis ha'Shekel," refers to the Shekel that was in use at the time of Moshe Rabeinu, which was equivalent to the "Sela" of the times of the Gemara. Machatzis ha'Shekel is half of a Sela, or two Dinarim. People became accustomed to calling the coin that was valued at half of a Sela, "Shekel," since it was "paid out" ("Shoklim" Oso) in order to fulfill the Mitzvah of Machatzis ha'Shekel each year (RAMBAN to Shemos 30:13).

4) [line 11] AVIV - early grain that is ripe enough to be eaten
5) [line 19] ASIF - gathering in of grain from the field
6) [line 39] HAFSAKAS IBURIN - it is the time from when it is no longer possible to make a leap year

7) [line 42] SHATA ME'ABARTA B'CHUSBENA TALYA MILSA - a leap year is dependent upon [seasonal] calculations (see above, entry #2)

8) [line 43] CHUSBENA HU D'LO SALIK LEHU L'RABANAN AD HA'IDNA - the Chachamim did not finish figuring out the calculations until now

9) [line 13] KITREI - rain clouds that converge

10) [line 26] OMER
(a) There is a Mitzvah to bring the Korban ha'Omer on the second day of Pesach. A large quantity of barley is reaped after nightfall after the first day of Pesach. At this time the grain is still moist, and the process of extracting one Omer (approximately 2.5 or 4.3 liters, depending upon the differing Halachic opinions) of barley flour is extremely difficult. The flour is baked and offered as a Korban Minchah on the 16th of Nisan. It is also referred to as the Minchas Bikurim -- Vayikra 2:14-16).
(b) In addition, a lamb is offered as an Olah, as it states in Vayikra 23:12.
(c) The Korban ha'Omer is the first offering of the new grain of the year, and as such it removes the prohibition against eating from the new grain.

11) [line 27] SHTEI HA'LECHEM
(a) The Shtei ha'Lechem is an offering of two loaves of bread (that are Chametz) that is brought on Shavuos. It is baked from the newly grown wheat (Vayikra 23:17). One loaf is given to the Kohen Gadol and the other is divided among the rest of the Kohanim in the Mikdash at the time. They are eaten on the day of Shavuos and the night afterwards, until midnight (RAMBAM Hilchos Temidin u'Musafin 8:11).
(b) Afterwards, all new wheat is permitted to be used for Menahcos.

12) [line 29] D'CHAYIL ME'URTA - [where the relevant Halachos of the new year] begin at nightfall

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