A nerd is a person who is obsessively interested in a topic, usually with the implication of a lack of social skills. A geek
bites the heads off chickens in circus sideshows is a common synonym for nerd. Traditionally, this obsessive interest focuses on the subjects of science, technology, computers, speculative fiction (e.g. Star Trek, Lord of the Rings, etc.), superhero comics, Dungeons & Dragons, and other non-mainstream hobbies (many of which have since turned mainstream e.g. superhero movies). There used to be a strong social stigma against geeks, but cultural shifts of geek-pride and acceptance starting in the late 1990s has both removed much of the stigma while rendering the terms near-meaningless through increasingly-broad overuse.
It would be pretty safe to say there are several nerds here.
- The secret origins of nerd, dork, and other things you've been called, io9
- Are 'geek' and 'nerd' now positive terms?, BBC
- xkcd on the "Can women be nerds?" debate (Basically, grow up.)
- xkcd on the difference between geeks and nerds