"Rosh Hashanah" literally means "head of the year," "rosh" being the Hebrew word for "head." It is considered to be New Year's Day by the Jewish calendar and also the beginning of the "High Holy Days" or the "Days of Awe." Tomorrow, the shofar will sound in synogogues all over the world. It's hard to explain how this very loud and somewhat awkward sounding trumpet can still bring tears to eyes and big smiles to the faces of young and old alike as it is sounded.
On this day and in the coming week, it is traditional to eat apples and honey for a sweet year to come and to say "L'Shanah Tovah," "For a good New Year," to everyone you meet. "L'Shanah Tovah" is the short version of a longer blessing said in greeting. The blessing says, "May you be inscribed and sealed for a good year." This probably seems quite odd to those who don't know the traditional literugy. The idea is that on this day all humans and the hosts of Heaven are judged by their deeds of the previous year and inscribed for blessings or hardships in the coming year in a kind of heavenly book. On Yom Kippur (literally, "Day of Atonement"), ten days later, after being given a specific chance to repent sins, the book is sealed for the year (because the idea is that up to that point what was written can be changed), hence the "sealed" part of the blessing.