A highly intelligent person, whose "nerdiness" is not necessarily restricted to one certain area of interest, but someone who has many varied interests and a vast amount of knowledge for all of them. Nerds are constantly learning and love to acquire new knowledge. Also, nerds do not announce to other people that they are nerds. This is something wanna-be nerds do, so if a person mentions a show they fanatically watch or a video game they play 24/7 and then gush "I'm such a nerd!", that person is actually a poser, does not deserve the esteemed title of Nerd, and most likely should be punched in the face. Just because being a real nerd is now cool, does not mean that you are.
Girl who has no idea what the capital of Minnesota is: Oh my god, I looooove Skyrim, I'm such a nerd!
Girl who knows all the countries, states, provinces and capitals of the world: I beg to differ. Excuse me while I go read War and Peace.