A convention, in fandom terms, is a gathering of fans. Why they gather is variable, but generally boils down to meeting new people, seeing old friends, and spending time with people who like what you like.
For non-fans, this may be hard to understand. Why travel 200, 500, 1000+ miles for that? Another wide variety of reasons. I'll use analogy.
Say, for example, you're an avid gardener. You watch HGTV, subscribe to BH&G, have a library of gardening books, and a pretty decent garden. You find out that there's this gardening club in your area, and they have meetings and presentations about, for example, how to build a better compost pile. You go, you meet some new folks, maybe make some friends, *and* you get some new tricks to try in your garden. Pretty cool. Then you find out there's a big regional gardening festival, where expert gardeners will be on hand to give workshops on how to turn clay into good soil, among other things. You think that would be great, so you decide to go.
That's not even close to a fandom con. Fans gather to meet people, as I said above, but also to see their favorite celebrities, from actors to authors to comic book artists and what have you. You can spend 3-4 days surrounded by People Like You -- which is something fans don't often get to do, because fandom is odd, and geeks are shunned.
Costuming is a huge part of fandom. There's something fun about walking around dressed as, say, Jack Sparrow or Gandalf or Harry Potter. It's a great conversation starter, too. There's a joke among costumers about the costumer's handshake: "Oh, hi, nice to meet you ... ooh, how did you *do* that?" I love the elaborate costumes, but I can't make them. Like these reference pictures and this costume. I'm not *that* good.
Cons are great fun for nerds. I love them so.