Happy New Year!
Not being Jewish, I don’t know much about it as a religious faith or a culture or a nation or whatever Judaism is, but I have a number of good friends who have no problems answering what I think are silly or stupid questions sometimes. Plus, there are some really good references out there for us non-Jews who make the effort to understand.
...In the seventh month, on the first of the month, there shall be a sabbath for you, a remembrance with shofar blasts, a holy convocation. -Leviticus 16:24
Rosh Hashanah occurs on the first and second days of Tishri. In Hebrew, Rosh Hashanah means, literally, "head of the year" or "first of the year." Rosh Hashanah is commonly known as the Jewish New Year. This name is somewhat deceptive, because there is little similarity between Rosh Hashanah, one of the holiest days of the year, and the American midnight drinking bash and daytime football game.
There is, however, one important similarity between the Jewish New Year and the American one: Many Americans use the New Year as a time to plan a better life, making "resolutions." Likewise, the Jewish New Year is a time to begin introspection, looking back at the mistakes of the past year and planning the changes to make in the new year. More on this concept at Days of Awe.
The name "Rosh Hashanah" is not used in the Bible to discuss this holiday. The Bible refers to the holiday as Yom Ha-Zikkaron (the day of remembrance) or Yom Teruah (the day of the sounding of the shofar). The holiday is instituted in Leviticus 23:24-25.
it is an interesting thing; next weekend is Yom Kippur, or the Day of Atonement. It is a day of fasting, prayer, and repentance. Reading about it makes me think of Holy Week during Lent, and even though it is considerably shorter (25 hours compared to 7 days) I suspect it’s a hard core sort of thing, in terms of observance.