The words Rosh Hashanah are mentioned in the Bible only once, in the Book of Ezekiel (40,1) but it is not certain that these words really refer to the specific holy day. In the Mishna there is a special tractate called Rosh Hashanah and deals with many aspects of this special memorable holy day.
During the long history of the Jewish people Rosh Hashanah was regarded as one of the most sacred and profound festivals. In the special prayers recited on these days, three main themes are emphasised - Kingdoms (malchuyot) which glorify the kingship of God; Remembrances (Zichronot) which remind us of all the great historical events occurred to the People of Israel by the will of the Almighty and ram's horns (shofarot) which also refer to the greatness of this awe-some day.
As Rosh Hashanah starts the Ten Days of Repentance, which culminate on the Day of Atonement, the sound of the shofar reminds every Jew that he must examine his deeds and repent and improve himself, being submitted to the judgement of God.
Biblical sources:
Leviticus 23, 24-25: "Speak to the Israelite people thus: In the seventh month, on the first day of the month, you shall observe complete rest, a sacred occasion commemorated with loud blasts. You shall not work at your occupations; and you shall bring an offering by fire to the LORD".
Numbers 29, 1: "In the seventh month, on the first day of the month, you shall observe a sacred occasion: you shall not work at your occupation. You shall observe it as a day when the horn is sounded."
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