Rosh Hashanah, Chapter Two, Mishnah 1. This mishnah presents us with a reality in which there were people, opponents of the beis din and the Sages, who sought to deceive the court and cause it to fix Rosh Chodesh on the wrong day. Because of this, procedures were established for examining the witnesses who testified about the new moon.
The words of the mishnah:
"Im einan makirin oso" - when the beis din does not recognize the witnesses and does not know who they are, character witnesses are required in order to verify their trustworthiness.
"Meshalchin acher imo l'ha'ido" - the Gemara explains that "another" means an additional pair, since two witnesses are needed as character witnesses for each of the witnesses of the new moon. They are sent together to testify about their character, that they are trustworthy and are not part of that same group of people - the Sadducees and those like them - who tried to deceive the Sages and bring them to establish Rosh Chodesh on a different day.
The background of the concern:
Whoever controlled the calendar was certainly in a very powerful position. The Sadducees had a different kind of calendar that they wished to follow: they wanted to ensure that the second day of Pesach, on which the Omer offering is brought, would always fall on a Sunday, since that is how they understood the verse. This was one of the reasons they sometimes sought to change the date of Rosh Chodesh.
"Barishonah hayu mekablin edus hachodesh mikol adam":
The mishnah adds the background for the need for the enactment. Originally, testimony about the new moon was accepted from any person. "Mishekilkelu haminin" - when the heretics carried out this corruption, the destructive act of attempting to deceive the Sages, namely that they hired people to testify that they had seen the new moon when they had not seen it at all. It is worth noting that the Tosfos Yom Tov discusses the possibility that "minin" is not the only word that could be used here, since there were various different groups.
Afterward, "Hiskinu shelo yehu mekablin ela min hamakirin" - the Sages made an enactment and decree that testimony about the new moon should be accepted only from people known to the beis din. And if they were not known to them, the beginning of the mishnah has already taught us that character witnesses known to the beis din may be sent to testify that these witnesses can be relied upon.
In summary: In this mishnah we learned the procedures for examining the witnesses of the new moon: originally testimony was accepted from any person, and once the heretics corrupted matters and hired false witnesses, the Sages enacted that testimony be accepted only from those who are known; and when the beis din does not recognize the witnesses, an additional pair is sent along with them to testify to their trustworthiness. In the background stands the importance of control over the calendar and the dispute of the Sadducees regarding the time of the Omer offering.