Jonathan Rauch's essay on introversion is a bit of an Internet classic, and I recommend you read the follow-up interview, too.
According to Rauch, the defining quality of introverts is that they find company exhausting: "My own formula is roughly two hours alone for every hour of socializing. [...] For introverts, to be alone with our thoughts is as restorative as sleeping, as nourishing as eating."
That sounds about right, but more fundamentally, I think the key to understanding introversion - and extroversion, for that matter - is need for external stimulation. I bet that if someone did a study on the relationship between introversion (which can be measured with self-report techniques) and the preference for riding a rollercoaster, he or she would find a strong negative correlation. Introverts are content with dealing with their own thoughts. I was an easy child to raise in one respect: I could play all on my own for hours on end. My mother later told me: "I made it a rule to come round to your room every half hour to see whether you were still alive."
Rauch says: "I'm not great at small talk, but I can seem quite outgoing for spells of up to an hour or so before I completely run out of gas." Oh yeah. I remember a friend of mine visiting me in England and quizzing me about how life there was. After half an hour or so my tongue literally started to hurt. I'm pretty sure that was a psychosomatic effect: It has never happened when I had to give a thirty-minute presentation on a topic I had prepared.
We aren't bad at talking. We are, as mentioned, bad at chit-chat. Rauch says: "I have to think about what to say next, and sometimes I can't think fast enough and end up saying something stupid. Or sometimes I just come up dry and the conversation kind of ends for while [sic] until I can think of another topic." I know the feeling, but I don't think that's the heart of it. John Althouse Cohen (who may or may not be an introvert) writes about why he hasn't blogged about certain topics: "Back when I was studying acting, I remember working on one scene and being told: 'Your third eye is going wild, John. [...]' Your third eye is that meddlesome little critic in your head who watches you and second-guesses every little thing before you're about to do it." I have long used a somewhat different metaphor: Filters. That's what's between your thoughts and your utterances. We've all met people (often drunks) whose filters seem to be completely broken. Intorverts' filters work too well.
Which may give you the impression that introverts are dull. I'd like to submit the opposite. I would guess that most people regarded as great thinkers were introverts. If you need constant outside stimulation, especially from other people, you're unlikely to write The Critique of Pure Reason or Ulysses.
So, give it a try! I earlier wrote a short post about how not to talk to introverts; here's the how-to: Give introverts something to react to. The easiest way to do this is to ask questions. You shouldn't overdo this (see above). A more sophisticated way is to bring up topics that the introvert can comment on. You might find there is a lot of interesting stuff in our minds; after all, we do a lot of thinking. We just need a little nudge to help us push it out.