Rosh Hashanah is the Jewish New Year — both a time of rejoicing and of serious introspection, a time to celebrate the completion of another year while also taking stock of one's life.
Rosh Hashanah ushers in the Ten Days of Repentance  (Aseret Yemei Teshuvah), also known as the Days of Awe (Yamim Noraim), which culminate in the fast day of Yom Kippur , the Day of Atonement. The Days of Awe represent the climax of a longer process. Starting at the beginning of the previous month, called Elul , the shofar  is traditionally sounded at the conclusion of the morning service. A ram's horn that makes a trumpet-like sound, the shofar is intended as a wake-up call to prepare for the Tishrei holidays. One week before Rosh Hashanah, special petitionary prayers called Selichot  are added to the ritual. Rosh Hashanah itself is also known as Yom Hadin  or the Day of Judgment, on which God opens the Books of Life and Death, which are then sealed on Yom Kippur.
Beyond services, Rosh Hashanah observances include:
- Eating a piece of apple dipped in honey , to symbolize our desire for a sweet  year, and other special foods  symbolic of the new year’s blessings.
- Blessing one another  with the words “Leshanah tovah tikateiv veteichateim,” “May you be inscribed and sealed for a good year.”
- Tashlich , a special prayer said near a body of flowing water to symbolically cast away sins.
And, as with every major Jewish holiday, after candlelighting and prayers, we recite kiddush and make a blessing on the challah.
The origins of Rosh Hashanah may be sought in a royal enthronement ritual of biblical times , though the Bible  itself never mentions the "New Year" or "Day of Judgment" aspects of the holiday. Even though Rosh Hashanah falls in the seventh month, later rabbinic  tradition decided to designate it the beginning of the year. Although the origin of this tradition may have been adopted from the Babylonians, the rabbis imbued it with Jewish significance as the anniversary of the day on which the world was created, or of the day on which humanity was created. Another explanation can be found in the significance of Tishrei as the seventh month, hence the Sabbath  of the year.
Challah eaten during the Rosh Hashanah season is round, symbolizing the eternal cycle of life, and traditionally dipped in honey to symbolize hopes for a sweet New Year. The same is done with apples. Some people avoid eating nuts at this time, since according to a somewhat convoluted Gematria  (mystical numerical interpretation) the Hebrew words for nut (egoz) and sin (het) have the same numerical value.
The Rosh Hashanah liturgy includes numerous prayers dealing with our personal, internal spiritual life and external behavior and conduct. Nearly every prayer and worship service is characterized by a special nusah, or body of musical themes and melodies.
The silent, standing Amidah prayers are filled with piyyutim, or religious poems, written and interpolated into the services over the span of centuries. Most of these poems emphasize the awesome nature of the coronation of God as king and speak of the inadequacy and terror of mere human beings in approaching God in prayer and praise. In addition, all of the Amidah prayers include entreaties to God to remember and inscribe the Jewish people in the book of life. On Rosh Hashanah, God records our deeds and on Yom Kippur God judges our spiritual fate for the coming year.
The evening services of both nights of Rosh Hashanah are relatively brief; in most synagogues they don't last longer than half an hour. The service starts with the Barchu and continues with the Shema and the blessings which precede and follow it. All throughout, the chazzan (cantor), together with the congregation sing a haunting tune reserved for the High Holiday evening services. The special Rosh Hashanah Amidah is then recited, followed by the recitation of Psalm 24 and the Aleinu.
Shacharit, the first part of the service, resembles the service of every Shabbat and holiday. After standard blessings, the Rosh Hashanah Amidah is then recited, followed by a lengthy repetition of the Amidah by the chazzan. When the chazzan concludes his repetition, the congregation rises for one of the most famous prayers of the holiday, the Avinu Malkeinu (“Our Father, Our King”), consisting of 20 lines of entreaties asking God to forgive our sins, to help us achieve repentance for our transgressions, to remember us favorably and so on.
In most communities, the Musaf service is prefaced by a passage recited by the chazzan requesting divine favor and permission to lead the congregation despite his or her deficiencies. A special Amidah is then recited that contains three unique sets of prayers: the Malkhuyot , which address the sovereignty of God, Zikhronot , which present God as the one who remembers past deeds, and Shofarot , in which we stand in nervous anticipation of the future. The shofar is usually sounded after the congregation silently concludes each of these blessings.
The Torah readings for Rosh Hashanah highlight themes of birth, creation and mercy through the story of the birth of Isaac , and raise issues of fear, judgment, and testing of faith in the telling of Isaac's would-be sacrific e. The first day's reading recounts how Sarah, at the age of ninety, gives birth to Isaac, her first and only child. In the haftorah we read about the birth of the prophet Samuel. Abraham's willingness to sacrifice his son in the Binding of Isaac  (Genesis 22 ), told on the second day, has come to represent the ultimate devotion to God. The haftorah, a reading from the Book of Jeremiah, talks about God's everlasting love
The brief afternoon service consists of the opening prayers, (the Torah reading if Rosh Hashanah falls on Shabbat,) the Amidah prayer, the chazzan's repetition of the Amidah, the recital of Avinu Malkenu and the concluding Aleinu.
Sounding of the Shofar
Several blessings are recited before the blowing of the shofar, then approximately 100 blasts are sounded throughout the worship services. The three different sounds are the tekiah (a single, long blast), the shevarim (three shorter blasts which together should be about the same length as one tekiah), and the teruah (nine staccato blasts, also about the same length of time as the tekiah and shevarim). Among the various reasons given for the blowing of the shofar is that the coronation of kings in ancient times was supposedly marked this way. Some view the sounding of the shofar as an alarm that awakens us to our need to do teshuvah , or repentance.
Although not officially a part of the synagogue service, an additional custom developed in medieval times called tashlich, which means “casting out.” On the afternoon of the first day of Rosh Hashanah (unless it is also Shabbat, in which case it is done the second day of the festival), Jews gather by a body of water, recite special verses and then throw crumbs of bread into the water to symbolically cast off their sins. Perhaps in an echo of the scapegoat ceremony, the fish are expected to eat the sin-crumbs and bear them away. A verse from the prophet Micah 7:19 — "You will cast away your sins into the depths of the sea" — is cited as the origin for this custom.
For more background about Rosh Hashanah, visit myjewishlearning.com or chabad.org.