Let's see, I'm no Rabbi, but I'll give it my best shot
Rosh Hashana is the name of this holiday in Hebrew. Rosh means head and Shana means year (Ha equals "the") so it is literally the Head of the Year.
It marks the start of the autumn holiday season with Yom Kipur and Sukkot coming soon. It's a 2 days sabbatical holiday, which means that religious people don't drive, light fire or anything electric etc. For the rest of us it means getting 2 days off work
Basically what you do is have a special feast with special dished and blessings. Some of these are head of fish or lamb (so that we will be heads and not tails), pomrgrenades (so that we will do as many good deeds as it has seeds), apple with honey (just to have a sweet new year). The one dish most people adhere to is apples dipped in honey.
Religious people then spend most of the holiday praying at the synagouge and when the new year comes in the evening they blow the Shofar (a special instrument made of ram's horn). By the way, in Judaism, the date changes at sunset and not at midnight so the new year begins at the evening.
Rosh Hashna also begins the countdown to Yom Kipur (day of atonement), which is 10 days later. These 10 days are deicated to lots of prayers and asking God to forgive us and also for people to ask forgiveness of each other and make peace among themselves.
That's about it I think. I'd be happy to try and answer any questions!