First of all, “geek” is slang, so it is much less about strict definition than it is about the associations that speakers have with the term and the people it is applied to.

Second, those associations have been changing quite a bit recently.

Third, some groups make distinctions between this word and some related words (principally “nerd”), while others treat them as synonymous.

So this is going to be a long answer, where I try to impart the associations that I have, and I have seen others have, using the word.

Anyway, with that in mind, “geek” was originally an insult, and is sometimes still used that way though that is diminishing recently. Specifically, it meant to imply that the geek in question shares some of the qualities associated with a particular stereotype.

That stereotype has been eroded recently, but we’ll start with the original stereotype, particularly its depictions in movies and television, which informed many English-speakers of the stereotype and thus which people could be called geeks. But first,

The “too long, didn’t read” version

Originally, geek was an insult referencing a stereotypical high school clique, associated with poor social skills and an unfathomable interest in math, science, or other technical and unpopular matters. It became more broadly applied to any kind of interest that others without the same interests couldn’t understand. Between the broadening of who could be considered a geek, and years of movies and television portraying geeks as the underdog protagonist, the term has been reclaimed, and many people now refer to themselves as geeks and would not be insulted by being called one.

Ultimately, however, its history as an insult means that it should be used with some care.

The original stereotype

“The geeks” are depicted, in media, as a kind of archetypal school clique, at least in America. The stereotypical depiction is a small and skinny (or, on the flip side, obese: primarily, not physically fit) white (both as in Caucasian, and as in being particularly pale) male, with neither talent nor interest in sports or physical activity, and a passion for science, mathematics, or other technical matters that his classmates do not share.

They are contrasted with various other archetypal cliques. Again, stereotypically, the geeks are a small group, close to the bottom of the social ladder, and often lack much social skill (read: awkward and nervous around girls, unable to convincingly stand up to bullies or even engender much sympathy from others while being bullied). They do tend to be portrayed with fairly close friendships within the clique, however. “The geeks” typically are contrasted with “the jocks,” the athletes, who are usually the most popular guys in school.

This, of course, mirrored reality to some degree, though no school is actually exactly as depicted in movies or television.

Now, while stereotypically, media frequently depicts geeks as being interested in technical matters, this was never (so far as I can tell) the true mark of the geek. For instance, being interested in car mechanics has almost never been seen as geeky: cars are cool, popular, even sexy, definitely not geeky. On the other hand, interest in superhero comics, video games and even more so tabletop games, fantasy and science fiction media, and so on have all been associated with geeks, even though these are not at all technical. It is far more about being interested in unpopular things than it is about math and science (though these subjects are typically fairly unpopular in adolescence).

Expanded application: any strong interest in an activity

The word geek is also appended to all manner of activities to indicate a very strong interest in it. “Drama geek” is a very common term for people interested in theater for example, for example. Note that more popular or physical activities are still rarely associated with the term, however, unless the interest goes well beyond what is popular. For example, dancing is quite popular; enjoying dance or being good at it is unlikely to be described as geeky. But someone who really gets into dance theory and practices dance regularly for its own sake might be called a dance geek (though I’ll admit I’ve never heard that particular usage).

Also, people who do something professionally, or at an expert level, are rarely described as geeks (unless one is discussing their origins); a movie star might say they got their start as a drama geek, but it would be unusual to call them a drama geek now. Ultimately, I suspect this is simply because the term was supposed to be an insult; it’s hard to insult someone’s interests when those interests make them money or are recognized as world-class.

Broadened demographics

Furthermore, the associations have changed with time. Non-white geeks (the Chinese or Indian geek has become almost as bad a stereotype as the original pale geek), female geeks, and physically-fit geeks have become much more common. Depictions of geeks with notable social skills are less common, but more often their social skills are depicted as merely “normal,” rather than sub-par.

Narrative role

It’s really important to remember that geeks were an important part of American movies and television. In particular, they served the role of the underdog protagonist in a lot of media based in American high schools (roughly age 14-18). They were bullied, socially anxious, and unpopular, which made them easy to relate to. This became especially pronounced as more interests could be associated with geeks, and geeks’ social ineptitude shifted to more typical teenager awkwardness.

Reclamation

In recent years, geek has become a largely reclaimed term. Many people proudly label themselves geek, including people who really wouldn’t have fit the stereotype and probably never would have had it used against them as a stereotype. “Geeking out” just means to get excited about something that doesn’t excite everyone, which almost anyone will do on occasion. Furthermore, the technical fields that were originally associated with geeks have become much more popular, thanks to the explosion of personal computers and the Internet.

These days, geekiness is a fairly popular trait, and being a geek is not really seen as being a member of a clique so much as just having interests particular to you that get you really excited. The primary qualification is that you can get excited about something, and have others be completely baffled by your excitement. For instance, I get really excited about new forms of web technology, mark-up languages, and programming. Plenty of people in my life would be completely mystified if I tried to explain why some development had me excited, though.

This definition, of course, is exceptionally broad, and almost anyone can self-label themselves a geek, and it’s become increasingly difficult to actually use as an insult if one were so inclined, because a lot of people see it as a good thing in the first place. For example, John Green has a fairly popular video which includes the following quote about how “nerd” is a weak insult:

…because nerds like us are allowed to be unironically enthusiastic about stuff… Nerds are allowed to love stuff, like jump-up-and-down-in-the-chair-can’t-control-yourself love it. Hank, when people call people nerds, mostly what they’re saying is “you like stuff.” Which is just not a good insult at all. Like, “you are too enthusiastic about the miracle of human consciousness.”

That said, this is a rather recent change in the popular understanding of the term, and some, particularly those who are older and grew up with its use as a negative, may still see it as an insult. Certainly, the original stereotype of a geek is fairly insulting.