Twitter is a micro-blogging platform. It asks users to share thoughts, 140 characters at a time. Everybody can find and read your tweets (that's what a message is called on Twitter) and you can do the same. It's not unlike sending a SMS to a friend, though with Twitter everybody can receive that message. It's like texting on a global scale!
First things first, to get started on Twitter you need an account. Go to twitter.com to get the process started.