Sunday night begins Rosh Hashanah, the Jewish New Year. L’Shana Tovah! (For a good year!) Chag Samech! (Happy Holiday!) It’s the beginning of 5773.
Rosh Hashanah occurs on the first of Tishrei. As usual with Jewish holidays, it begins at sunset. It is celebrated for two days everywhere. An earlier article here mentioned why we often celebrate holidays for one day in Israel and two in the Diaspora. Because the Sanhedrin had to declare the new month by the moon phases, and as our ancestors spread out from Israel, it was too distant to get the message out fast enough, so they often observed holidays for two days to be sure they got it right for one of them. For Rosh Hashanah, messengers were not dispatched even in Israel, thus they also celebrate for two days.
Much of the holiday is spent at the synagogue, where we listen to the blowing of the shofar. There are 100 notes sounded each day in specific patterns.
Another tradition is to have apples dipped in honey, signifying our wish for a sweet new year. Challah is usually baked in a round shape, instead of the usual braid. Many people also dip the challah in honey.
Rosh Hashanah is the beginning of the High Holidays, a series of holidays that extend for almost a month.
You can read more about the holiday at Judaism 101, the source for most of this article, or on Wikipedia.