What is the purpose of the holiday Rosh Hashanah?

It celebrates the Jewish new year -- the day that God created Man in his own image (according to tradition, 5778 years ago).

Answer:

Rosh Hashanah is the first two days of the month of Tishrei, and is the Jewish New Year. Our traditions state that at that time the world is judged for the coming year (Talmud, Rosh Hashanah 16a). The shofar (ram's horn) is blown (Leviticus 23:24; Talmud, Rosh Hashanah 33b-34a), symbolically heralding God's kingship, and festive meals are held in the home.