Before us is Mishnah 3 in the first chapter of Maseches Rosh Hashanah. The Mishnah lists six months of the year in which messengers would go out from Jerusalem to the Diaspora, in order to inform the communities there on which day Rosh Chodesh had been established. The festivals of the year depend on the fixing of Rosh Chodesh, and without this information the communities of the Diaspora would not know when to observe them.
The six months for which the messengers went out:
"Al Nisan - mipnei haPesach" - so that the people of the Diaspora would know when Pesach falls, since it depends on the day on which Rosh Chodesh Nisan was fixed.
"Al Av - mipnei haTa'anis" - because of Tishah B'Av.
"Al Elul - mipnei Rosh Hashanah" - since the following month is Tishrei, and Rosh Hashanah depends on the day on which Rosh Chodesh Elul was fixed.
"Al Tishrei - mipnei takanas hamo'ados" - the fixing of the festival days of that month: Yom Kippur, Sukkos and Shemini Atzeres.
"Al Kislev - mipnei Chanukah" - in order to know when the twenty fifth of Kislev falls.
"Al Adar - mipnei haPurim" - in order to know when Purim falls.
"Ucheshehayah Beis HaMikdash kayam, yotz'in af al Iyar mipnei Pesach katan":
At the time when the Beis HaMikdash stood, the messengers would go out for the month of Iyar as well, because of Pesach Sheni. Someone who did not have the opportunity to bring the korban Pesach at its proper time in Nisan was able to bring it on the fourteenth of Iyar, and he needed to know its exact date in order to travel up to Eretz Yisrael and to Jerusalem for this purpose.
In summary: The Mishnah teaches that in six months - Nisan, Av, Elul, Tishrei, Kislev and Adar - the messengers went out from Jerusalem to inform the Diaspora of the fixing of Rosh Chodesh, because of the festivals and special days that depend on it; and when the Beis HaMikdash stood, they went out for Iyar as well, because of Pesach Sheni.