Twitter in a nutshell
Twitter is a messaging platform, also referred to as micro-blogging. Information is exchanged between users in the form of messages comprising 140 characters or less. Updates are sent and received via web, SMS or third party applications like Twhirl. The basic idea is you choose who's updates you want to follow, and others choose to follow your updates. Updates are fed into your feed where you can see what the people you follow are doing. Conversely, your updates are sent to your followers feeds.

Twitter is used in different ways by different people. It's used as a way to let your friends know what you're doing at any given moment. It's a way to reach bloggers and opinion leaders. It's a way to position yourself as an opinion leader. It's great for driving traffic to web pages. It CAN be a great tool to use in a social media marketing campaign, IF it's used properly and not abused.

More than anything, Twitter is a community. It's a community of people who are passionate. Many are bloggers, all are influential communicators to some degree or another. Twitter enables word of mouth to spread at lighting speed. It's a community of people who, if you SPAM them, will at best ignore you, at worst completely slam you. There's a whole site called Stop Twitter Spam dedicated to helping people Twitter responsibly. It's also a community of people who will sing your praises, on Twitter, through blogs and via word of mouth if you engage them in a meaningful way.

Some great examples of brands using Twitter effectively
@Zappos - Online shoe company Zappos CEO Tony Hsieh. Tony is a much-loved and widely followed Twitter user. He currently has over 4,000 followers. Those 4,000 followers are customers, fans and bloggers. Tony uses Twitter to let people know what he's up to, as a person, and also as a way to let people know when something interesting or exciting is going on at Zappos. He's run contests through Twitter, used it to connect with fans in various locations through "Tweetups" (meetups organized through Twitter.) Most importantly, he has engaged the Twitter community in a two-way communication stream. He listens and responds to his followers. He's so fond of the service that he's created an entire page on the Zappos website.

@HRBlock H&R Block is using Twitter as a customer support mechanism. As a result, they've gotten tons of positive attention from bloggers, like here and here and here.

How to use Twitter responsibly
So how can a brand use Twitter responsibly and effectively? Easy, take the time to get to know the ins and outs of the community and be human. Don't use Twitter as a means to boast about your brand or service, use it as a tool to interact with the community on behalf of your brand or service.

Have more examples of brands who get it? Have some pointers that I haven't covered? Think I'm full of it? Comment and let me know.

PS
Feel free to follow me on Twitter.