The definition that I like is a nerd is someone who is good at something but lacks social skills. This is in contrast to a geek (excels at something and has social skills), a dork (doesn't excel and has no social skills) and a normie (doesn't excel but has social skills.)
Being a "nerd" means what? Because it has no correlation to intelligence, and is purely a social label, generally self-inflected/self-assumed.
Edit: public high school