Thank goodness this gentile (me) still has time to make her New Year's Resolutions... but if I was Jewish, I would have celebrated "New Years" about a week ago.
The Jewish "New Years" is known as Rosh HaShanah. Here's a little Hebrew lesson to help you understand the name of the holiday: Rosh translates to "head," Ha translates to "the" and shana is the Hebrew word for "year." Put it all together and what do we have? The "head" (or 'beginning') of the year.
Rosh Hashanah is celebrated for two days because for Jews, it is too important of a holiday to be observed for just one day- this, after all, is the day commemorating God's creation of man.
Here's a fun fact about the holiday: people typically eat and pass out apples dipped in honey as a wish or blessing that friends and family will have a sweet, new year. :)