
According to Wikipedia:
Micro-blogging is a form of blogging that allows users to write brief text updates (usually 140 characters) and publish them, either to be viewed by anyone or by a restricted group which can be chosen by the user.
That means that you could send short messages to a variety of devices, such as cell phones, BlackBerry or iPhone, but can also be viewed via IMs and email.
No matter where you are, at your desktop, travelling or at work, you can send a short message about an event, a meeting or anything you would like to broadcast quickly.
http://twitter.com appears be one of the most popular service out there, but often goes down, the creators sometimes disable the 'Reply' link, especially when there is live event going on, where a lot of people are logged in.
A new comer to this area is http://identi.ca, which could be a competitor to Twitter, but has lots of catch up to do - It has yet to add a reply link.
Micro-blogging has yet to hit the mean stream, but hopefully, with enough users and more true micro-blogging sites, we will all be connected in real time, reading or writing brief messages.