Mishnah/Seder Moed/Tractate Rosh Hashanah/Chapter 1/4
Seder Moed, Tractate Rosh Hashanah: Chapter 1, Mishnah 4
In the previous mishnah, the subject of Jews living in the Diaspora was discussed and how the Rabbis dealt with the problem of them not being able to know when the Sanhedrin declared Rosh Chodesh. If Rosh Chodesh fell on Shabbat, however, there was a problem as one is prohibited from traveling on Shabbat. Would messengers get sent? This mishnah discusses that subject.
Hebrew Text 
- על שני חודשים מחללין את השבת, על ניסן ועל תשרי
- שבהם שלוחים יוצאים לסוריה, ובהם מתקנים את המועדות.
- וכשהיה בית המקדש קיים--מחללין אף על כולם,
- מפני תקנת הקרבן.
English Translation 
- On two months they desecrate the Shabbat, on Nisan and on Tishrei.
- For in those months, they were sent out to Syria to correct for the festivals.
- And when the Temple existed, they desecrated Shabbat in all of them--
- To correct for the sacrifices.
Syria: The Mishnah uses "Syria" as a euphenism for the Diaspora.
Correct for the festivals: Pesach, Shavuot and Sukkot are the most important holidays (besides Shabbat) on the Jewish calendar. The Rabbis considered it important enough that they be observed on the right day that they allowed people to desecrate Shabbat in order to propogate messages regarding Rosh Chodesh Nisan for Pesach and Rosh Chodesh Tishrei for Sukkot. While Shavuot is in Sivan, one can easily deduce when Shavuot is easily as it is a week of weeks (i.e. 7 weeks; 49 days) after Pesach.
Correct for the sacrifices: Special sacrifices were offered on Rosh Chodesh, so while the Temple existed, they allowed people to desecrate Shabbat whenever necessary in order to deliver messages regading Rosh Chodesh, so that the sacrifice might be offered on the correct day.