On Pesach the world receives a judgement on the grains. On Shivuos the world receives a judgement on the fruit of the trees. On the first day of Tishrei people of the world receive judgements as sheep passing through a gate. On Succos the world receives a judgement on water.

Rosh Hashana 1:3

The mitzvah of Kiddush Hachodesh is having two witnesses come to Bais Din and say they saw the new moon. Bais Din uses this information to establish that day as Rosh Chodesh, the first day of the month. Then Bais Din sends out messengers to say which day they made Rosh Chodesh.

Bais Din sent out messengers on 6 months.

1. Nissan so people would know the correct day to start Pesach.
2. Av so people would know the correct day for the 9^th of Av.
3. Elul so people would know the correct days for Rosh Hashanana.
4. Tishrei so people would know the correct days for the Yom Tovim.
5. Kislev so people would know the correct days for Chanukah.
6. Adar so people would know the correct day for Purim.

During the time of the Bais Hamikdash, they also sent them in Iyar so people would know when to make Pesach Sheni.