Naadam is the big festival held in July in Mongolia. It consists of the "three manly sports" - horse racing, archery, and of course, wrestling. Despite the name, women compete in archery as well as men, and it is actually children - both boys and girls - who are the jockeys for the horse races.
Naadam itself just means "festival," and one can various types of naadams and have them any time during the year. Nevertheless, when people talk about Naadam without additional clarification, they mean the festival held July 11 - 13. The main, national Naadam is held in Ulaanbaatar, but aimags (provinces) and even smaller areas also hold their own festivals.
I've actually been in Mongolia for five Naadams, but have only gone to two in person. While a lot of fun, to me they are also a bit like any sporting event in the US. If you really want to see what's happening, it makes more sense to watch it on TV. In 1999 I attended the national Naadam in Ulaanbaatar, and in 2004, I attended a local Naadam in Harhorin while travelling with a tour group. (I was their resident academic.)