It depends on how you use the terms. In the general way that most people use the terms, I'd probably be seen as an extrovert since I have no problems interacting with others in large group settings and enjoy speaking in front of an audience. I'll readily initiate a conversation, or introduce myself, if I'm in a situation where I don't know anyone. In the Meyers-Briggs sense of the terms, though, I'm definitely an introvert.
A bit of explanation (what can I say--I'm a teacher ) In Jungian/MB theory, introversion and extroversion aren't discrete categories--they represent ends of a continumn and most people are positioned somewhere along the scale instead of being at the ends. The terms, in the Jungian/MB sense, also represent inherent preferences that are present at birth, much like right-and left-hand preference. Over time most people can train themselves to use their opposite hand, especially if circumstances dictate that working against preference is desirable or advantageous. I chose a career that prefers extroverts so I've grown quite adept at "working in my wrong hand". The difference between a true extrovert and a "closet" introvert is usually in the degree of energy it takes to handle social situations.
Angie has hit on it in her description of how being with people provides her with a rush of energy--her batteries get charged by being with others instead of being drained by her interactions. A "closet" introvert, like me, however has to move into a social situation with a store of energy because the longer I'm with a group, the more I fizzle out.
And, by the way, shyness is a totally different trait. There are shy extroverts who dislike interacting with large groups and who cringe at the though of public speaking, and there are non-shy introverts, like myself, who go out of their way to talk to strangers and who enjoy public speaking.
ETA: My students were sometimes surprised to learn that extraverts often found extended periods of being alone to be quite stressful. Since they have an outward focus, extraverts have trouble staying motivated and engaged if they aren't able to connect with others on a regular basis. An extravert can enjoy periods of quiet and reflection, but extended periods of being alone aren't easy for them.
