Diwali is the "celebration of lights" and is celebrated to signify the victory of good against evil. A long, long time ago, there was a battle of two families and one was sent to exile. After their agreed upon 12 years was up, and they returned to take over the kingdom, everyone put their lights on to guide them home and welcome them. (Yes, I am paraphrasing this from a website to ensure accuracy, HOWEVER I did actually learn this in my Religions of India class!! The story of the two families battling is from the epic Mahabharta that we are currently reading...don't quote my spelling of that...)
It is also said Diwali is the birth date of the goddess of wealth, Lakshmi. So, on the date of Diwali, you are supposed to leave your lights on so that she visits you and brings wealth. Another tradition is that it is lucky to buy a dish on Diwali. Why? I don't know.
Anyways, Happy Diwali!