I tell my story of being an introvert a lot because, well honestly it's a major defining characteristic for me. It's also helpful that I explain that to people because I've found that things I do can be misconstrued if I don't explain myself. I've had people call me unfriendly, or believe I don't like them, so explaining my introversion ahead of time allows them to have an understanding of what they can expect from interacting with me before they start making judgements.
I really believe that introversion is still one of the most misunderstood personal characteristics there is. When I tell people I'm an introvert they'll actually say things like "no, don't say things like that about yourself." This leads me to believe they see it as an affliction rather than a personality characteristic.
Being introverted means I get tired of interacting with people after a while. It's nothing personal, but I just want some alone time. I don't require much at all to be content, so I view it as a positive. I've met extreme extroverts who say that they feel depressed when they can't be around people for extended periods of time. I'd say that's something I'm glad I don't have to deal with.
Introversion is not the same as being quiet or shy, although they are often put in the same bucket.
To learn more about some of the memorable introverts of history pick up the book "Quiet: The Power of Introverts in a Word that Can't Stop Talking."