Wasn’t one enough?
In the Diaspora (outside of the land of Israel) many Jewish holidays are celebrated for two days. That’s because in ancient times, the Jewish calendar was originally based on the observation of the moon from the Temple Mount. It took a long time to get the announcement of the New Moon to Diaspora communities, so there was uncertainty about holiday dates.
But Rosh Hashanah is observed for two days even in Israel! The reason for this is that the the moon’s cycle is 29 1/2 days. Elul, the month before Rosh Hashanah, might have had 30 or 31 days, depending on exactly what the moon was doing that year. So there were two days of Rosh Hashanah, just to be sure to get it right.
Now, you may be wondering why it is that we do this even though we have calendars that know the exact dates years, even centuries, in advance. The answer is that the custom became established very early, at least before the year 70 of the Common Era and perhaps much earlier. Many Jews are reluctant to alter a custom that is so old, and refer to the two days of Rosh Hashanah as a Yoma Arichta, Aramaic for “one long day.”
However, as with many things in Jewish life, there is another custom, in some Reform communities, to celebrate Rosh Hashanah only on one day, now that we can calculate the New Moon accurately. They argue that the Torah prescribes one day of Rosh Hashanah, so they celebrate for one day.
By the way, if you need a Jewish calendar, there is a good one at the Hebrew Jewish Calendar website.