Well, as an introvert myself, I'm not sure if I can really explain it to someone who is not one. You just often feel like you want to be by yourself, or only around people you know really well, like your family and closest friends. It is not that you are afraid or anything, which is more shyness, but just that you don't feel like it. If I have to I can socialize and pretend to be enjoying it, but I really don't.
Introverts love spending time thinking about things more carefully. They don't care so much about showing off to others. I think the world needs more introverts to tell you the truth since they are often the ones who create new things and make the world a better place.