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God's breath
The shofar is the sound of man's breath as it is blown into a ram's horn. Man is the sound of God's breath as it was blown into the dust of the earth. On the anniversary of man's formation God wants to see the results of His blast. He tells man to blow back the breath of God and listens carefully to the sound. It should still be reminiscent of God's own breath.

SHOFAR
A shofar is an instrument made from the   more...horn of a ram or other kosher animal. It was used in ancient Israel to announce the New Moon (Rosh Chodesh) and call people together. It was also blown on Rosh Hashanah, marking the beginning of the New Year, signifying both need to wake up to the call to repentance, and in connection with the portion read on the second day of Rosh Hashanah, the Binding of Isaac (Genesis, chapter 22) in which Abraham sacrifices a ram in place of his son, Isaac.

Today, the shofar is featured most prominently in the Rosh Hashanah morning services. It is considered a commandment to hear the shofar blown.
There is a great deal of symbolism tied in with the legal requirements for what constitutes a proper shofar. The shofar of Rosh Hashanah, whose purpose it is to rouse the Divine in the listener, may not be constructed of an artificial instrument. It must be an instrument in its natural form and naturally hollow, through whom sound is produced by human breath, which God breathes into human beings. This pure, and natural sound, symbolizes the lives it calls Jews to lead. What is more, the most desirable shofar is the bent horn of a ram. The ram reminds one of Abraham's willing sacrifice of that which was most precious to him. The curve in the horn mirrors the contrition of the one who repents.

In the Talmud, we read: Why do we sound the shofar? Because the Holy One, blessed be God, said: Blow me a ram's horn that I may remember to your credit the binding of Isaac, the son of Abraham, and I shall account it to you as a binding of yourselves before Me. The Torah tells us: Abraham looked up and behold, he saw a ram caught in the thicket by its horns [Genesis 22:13]. This teaches us that the Holy One, blessed be God, showed our ancestor Abraham the ram tearing himself free from one thicket and becoming entangled in another. Said the Holy One, blessed be God, to Abraham: Thus are your children destined to be caught in iniquities and entangled in misfortunes, but in the end they will be redeemed by the horns of a ram. Therefore the prophet Zechariah said of the time of redemption: And YAHWEH shall be seen over them, and his arrow shall go forth like the lightning; and YAHWEH God shall blow the shofar, and shall move in stormy winds of the south [Zechariah 9:14]. [Rosh Hashanah 16a]

What is a Shofar?
A Shofar is long Rams horn used to proclaim Jewish ceremonial events. It is hollowed out and blown on one end similar to a trumpet. The Ibex is one the most popular rams horns. They usually appear conical with a spiral appearance.

According to the Talmud, a Shofar that is legal for ceremonial events must be at least three handbreadths long.

There are small Shofars that people sometimes use which are not really Shofars by Talmudic definition. To be accurate so you can use the generic term "Keren", which means "horn" in hebrew.

The Shofar goes back far into biblical history. It is believed that the Shofar commemorates the Ram caught in the thicket by its horn (Hebrew: Keren). …
In the absence of the temple today, the Shofar is used instead of the Chotzotzerah to proclaim the Jewish high holy days. The holy day, "Rosh HaShannah" or New Year is also called Yom HaTeruah.

In many translations, this is referred to as the feast of the trumpets.

"Yom" means "Day", "Teruah" means to blow the trumpet or sound alarm.  less