Mesechtas Rosh Hashana talks about two main topics. The first, is Kiddush HaChodesh, Beis Din declaring the new moon each month. The first two perakim describe in detail the process. The witnesses, how Beis Din checks them, declaring Rosh Chodesh and letting everyone in Klal Yisroel know that the new month has begun.
The second half of the Mesechta talks about Rosh HaShana. First it describes the type of shofar we can use, then where and when we blow the shofar.
The final few Mishnayos talk about the specific way we blow the Shofar during the Mussaf.
Finally, the last few lines of the Mesechta tells us about whether each person must daven on their own or whether the Chazzan can daven on your behalf (just like we have someone blow shofar for us).
(ט)...
כְּשֵׁם שֶׁשְּׁלִיחַ צִבּוּר חַיָּב,
כָּךְ כָּל יָחִיד וְיָחִיד חַיָּב.
רַבָּן גַּמְלִיאֵל אוֹמֵר,
שְׁלִיחַ צִבּוּר מוֹצִיא אֶת הָרַבִּים יְדֵי חוֹבָתָן:
(9) .. The Tana Kama Taught:
Just as the Chazan is obligated to daven
so to each and every person is obligated to daven on their own (this means we cannot rely on the Chazzan).
Rabban Gamliel disagrees and says:
each person is not obligated to daven on their own. rather, the Chazzan can daven on your behalf (meaning, the Chazzan's davening fulfills my own obligation.