I can remember, a year ago, when I was a budding blogger, I was completely annoyed looking twitter badges in each and every blog I visited. All blogs with some unique badges read "Follow us on twitter". I didn’t know what twitter was.. After few months, I was over whelmed to know what exactly it was that made every bloggers make use of it. After working on it for a fortnight or a month, I came to the conclusion – "Micro blogging". Twitter can be called as a "platform for micro blogging".
For instance, you want to know what exactly your friends are doing right now or vice versa. But it is not possible for your friends to mail you or blog about each and every thing they are doing.. It would be too time consuming and clumsy task. But twitter is a micro blogging platform where all such things can be made possible. You just need to open an account and start follow your friends, after that all their updates will be visible to you. It is like sending a group SMS to everyone who are in your network. Here you can post updates of upto 140 characters long and every one following you will be able to view those updates from you. The best part is that, unlike Instant messengers, there are several ways available to post messages (also called tweets) – from web, desktop clients (like Twhirl), mobile clients, SMS, etc. Initially you start with their website, later I’ll say about some good twitter clients.
So, if you believe us then just open an account at twitter and start following some friends. You will see that, within months, you too will be addicted to twitter. 
To get started, you can follow DevilsWorkshop updates @rahul286 and my personal updates @deepakjain1989
For better understanding, you can have a look on this ‘How-to’ video by Leelefever.
Links: Twitter | Registration
