My first lesson on the subject was that it is a dysfunctional utopia. The Giver is often listed as a prime example of a dystopia, and it fits the bill. Imagine an absolutely perfect utopia - no pain, no violence, everyone is the same, everything is fair, everyone is happy. And then, of course, are the dark underpinnings that the society is built on, thus the dysfunctional part of the dystopia.
But not all of the dystopias I've read lately have any kind of utopian element. For instance, the Hunger Games. Yes, there is a lot of happiness and carefree-ness in the capital, so maybe that's where it comes in. Would you say the capital is a utopia, though? I wouldn't, not really.
Another example I'm thinking of is a book I'm currently reading, The House of the Scorpion. Not a utopia in any way for anyone.
So my current definition of a dystopia is:
A fictional work dealing with what our society could potentially become if we keep going down a path that we are currently on, sometimes with a utopian element.
Okay, so that's my definition. Now, I'd like to hear yours.