Adonai said to Moshe, "Tell the people of Isra'el, 'In the seventh month, the first of the month is to be for you a day of complete rest and remembering, a holy convocation announced with blasts on the shofar. Do not do any kind of ordinary work, and bring an offering made by fire to Adonai.'"
The Hebrew word rosh means "head". The prefix ha means "the". The word shana means "year". Thus the name translates to "head of the year". This day is also called Yom Teruah, which means "day of trumpets".
There are two traditional answers. The first is that there was an agricultural calendar from pre-Sinai days that started the year in the fall, and the ancient Israelites kept the fall as the head of the year. (Exodus 34:22 mentions a "feast of ingathering at the turn of the year.") Also, tradition teaches that Rosh Hashanah is the anniversary of the sixth day of creation when Adam was created (the ancient Rabbis decided that because the numerical value of y'hee ("let there be") in the creation account was 25, creation must have started on the twenty-fifth day of the month of Elul).
Rosh Hashanah begins the ten Days of Awe: the ten days until Yom Kippur which are for introspection, repentance, and making amends with others. Tradition says that on Yom Kippur our fate for the next year will be decided, and those who will live through the year will have their name inscribed in God's book of life. The traditional greeting is L'shanah tovah tikatev(i) v'taihatem(i), meaning "may your name be inscribed for a good year" (the alternate (i) endings are the grammatical form used when addressing women). Rosh Hashanah focuses on the majesty and sovereignty of God to begin this time of repentance, and the shofar blasts wake us up to the need for repentance.
This day foreshadows the rapture, an assembly called by blowing of trumpets to assemble before God in a renewed state.
Notice that this day is called a memorial. What are we remembering with the shofar blasts? According to tradition, this day is the anniversary of the beginning of creation! Job 38:7 mentions that during creation "all the sons of God shouted for joy". We should do this again!
Days that are memorials are also often a time for renewing commitments. What commitment comes with creation? The creation story implies an initially pure relationship with God. Pray about regaining this, with introspection and repentance, making amends to other people and to God.
In Matthew 19:21, Yeshua tells the rich young ruler, "If you want to be perfect..." To the Judaism of that time this idea would be either nonsense or sacrilege! The Mosaic Law was to make us holy (set apart), not perfect! Who could be perfect? Yet Yeshua was speaking truth, because his covenant starts the re-creation of the world. This is also worth celebrating!
Tradition asks us to examine our past year, and dedicate ten days to introspection and repentence. How do our lives show evidence of being part of God's re-creation of the world? How can we better appreciate the majesty and sovereignty of God? How must we, in our role as priests, purify ourselves so we can better intercede for others and for our communities?
Since Jewish believers are part of the covenant of Sinai, a Messianic Jewish congregation still has a holy convocation, the blowing shofar blasts, and a sabbath from work.
One of the most common Rabbinical Jewish traditions for Rosh Hashanah is to eat apples with honey, to help us remember to pray that the upcoming year be sweet. Many Messianic Jewish believers also keep this tradition.