This is the Jewish New Year and it is observed in the synagogue with the sounding of the shofar. It lasts for 1 or 2 days and it is considered a time of introspection. The most common custom is to dip apples in honey to signify purity, happiness and hope for a new year.
Regular Websites
Presents videos, customs, history, recipes and an image gallery. - History.com: Rosh Hashanah
http://www.history.com/content/roshhashanah
Provides a list of dates, the history, customs, greeting and observances of this holiday. - Judaism 101: Rosh Hashanah
http://www.jewfaq.org/holiday2.htm
My Jewish Learning: Rosh Hashanah
Contains information about the shofar, holiday customs, Tashlikh, the ten days of repentance and recipe for Rosh Hashanah honey cake. - My Jewish Learning: Rosh Hashanah
http://www.myjewishlearning.com/holidays/Jewish_Holidays/Rosh_Hashanah.shtml