2 days, but Reform Jews celebrate 1 day.
Rosh Hashanah is celebrated for 1 day inside Israel and among Reform Jews, and 2 days for non-Reform Jews outside Israel.
It celebrates the Jewish new year -- the day that God created Man in his own image (ostensibly 5769 years ago). It is the holiest day in Judaism.
Rosh Hashanah is the Jewish new year. Rosh Hashanah literally translates to 'Head of the year'.
Rosh Hashanah was on October 3rd in 1959.