Rosh Hashanah is the Jewish new year (it is currently the year 5772) and comes this secular year (2012) on the 17th of September. The Jewish calendar is more similar to a lunar calendar and as a result does not correspond with the Gregorian (secular) calendar.
It literally means "head of the year". Jews around the world celebrate it on the same day.
It begins the High Holy Days which end with the very solemn Yom Kippur 10 days later. (The intervening days are referred to as The Days of Awe.)
Rosh Hashanah is a joyous holiday and is celebrated with sweets - Typically apples and honey, jelly donuts and the like.