When the Beit HaMikdash stood, it was essential for the kohanim in the Temple to know whether the new month began on the 30th day or the 31st day after the previous Rosh Hodesh, so that they would know when they had to bring the special Mussaf sacrifice for Rosh Hodesh. This was so important that the Sages taught that it would be permissible for witnesses who saw the new moon to travel to the Temple to testify even if it was Shabbat and their travel would involve hilul Shabbat (transgressing the Sabbath). After the destruction of the Temple, Rabban Yohanan ben Zakkai ruled that this hillul Shabbat should only be limited to situations when it served an essential purpose. Without the Temple sacrifices, it was deemed essential only for the months of Nisan and Tishrei, when it was necessary to establish the date of the holidays of Pesah, Yom Kippur and Sukkot.
The Gemara learns the rule permitting hilul Shabbat from the passage in Vayikra 23:4, which emphasizes the need for the holidays to be established in their proper time. The Ritva understands this to mean that really every Rosh Hodesh deserves to be established on time – irrespective of the need to bring the appropriate sacrifice – even if Shabbat must be transgressed in order to assure that. Nevertheless, the Sages limited that Biblical leniency to just two months of the year.
What the Mishna specifically teaches is that for the purpose of establishing the two months of Nisan and Tishrei at the appropriate time, messengers are sent to Suria. The Suria mentioned in the Mishna is the Biblical area to the north of Israel, known as Aram Damesek and Aram Tzova. We find that Suria has a unique status in halakha with regard to many halakhot, not only because of its proximity to the Land of Israel, but because it was part of the northern Kingdom of Israel under several kings during the period of the First Temple. Furthermore, some opinions suggest that the northern border of Israel extends well to the north of the Jewish settlement in Israel during the Second Temple period. There was also a large Jewish population center there, and some of the political leaders there were descendants of Jews (like the grandchildren of King Agrippas) or were closely allied with them.