People always think of nerds as the dorky kids with the thick glasses who like doing trigonometry. But really, nerds are just people who are really educated on a subject and are sometimes extremely passionate about it. Some people's nerd obsession is math related things, other people it's the color of Legolas's hair.
Now, nerds are not to be mistaken with geeks. Geeks are just passionate about things. They're the people in the crazy fandoms who go all out on their Halloween costumes so that they look as much as the 11th Doctor as possible while their friend goes as Dobby. Geeks and nerds are similar, but not quite the same.
Nerds are the smart ones, geeks are the crazy ones.
(Speaking of nerds, I may have found a shirt I need.)