Twitter can often be a confusing mess. Once you've started following 10 or more people, it becomes really difficult to keep up with all the updates. The further you scale up, the less practical it becomes to read every single post, and then of course important information might slip past undetected. Even worse, some people post updates constantly, and searches for real-time news, which Twitter excels at, updates far too quickly to be read. Twitter allows users to create lists in order to filter users, but the website interface is clunky at best.
The solution lies in separating Twitter as a service from its own website. If it wasn't for mobile phone clients, we'd never have the kind of real-time updates and photo sharing that we do today. Similarly dozens of third-party clients exist for the desktop, which improve upon the default experience in some way. Tweetdeck's genius feature is the organization of Twitter lists into columns that are displayed simultaneously and can be read at a glance. You can also quickly create and edit lists, allowing you to weed out people who spam your timelines and cultivate those posts are genuinely useful. Search results are displayed in their own columns, which can easily be left visible or knocked off when they aren't useful anymore. Most importantly, you can immediately see when you have new mentions and direct messages, which are easy to miss on the website.
Tweetdeck has completely changed the way I use Twitter. I once dismissed Twitter entirely, not seeing the whole point. Now, however, I have one monitor on my desk with Tweetdeck maximized at all times and I genuinely feel more productive. There's one column for followers' updates, one for PR and journalists, one for corporate accounts, and several for current trends and stories I might be interested in following. More than Twitter it self, Tweetdeck has improved the way I work.