The thing with Twitter is this - a lot of people don't get it at first. It took me at least two or three times to get 'into it', but that's because the web interface isn't as good as some of the desktop tools (Tweetdeck, Seesmic) or iphone (Tweetie) but also because it takes some effort - following, getting followers, or both.
Think "Field of Dreams" (if you build it, they will come) - too many people setup a Twitter account, and just do nothing except wait, and wait, and wait....
As with all Social Media, it pays to consider a strategy first - what are you looking to achieve? Reach out to customers? Engage with similar companies? Research articles?
I'd suggest for business, Twitter falls into 3 general brackets.
1) Following - inspirational or interesting people/companies
2) Building followers - existing or potential customers
3) Publishing content into the Twittersphere, in the hope someone will search for something you're supplying, or can help them with.
I'd suggest best way to 'get into it' is set up a personal account, get used to it, then establish a business profile.
Twitter does work for business, and it works extremely well - often in mysterious, unexpected and sometimes creepy ways. For us, it works for publishing content, searching for new leads/clients, keeping up with the news and happenings, networking, tracking competitors, spotting trends, but above anything else, keeps things fresh, modern and up to date.
Have a look at our profile and see if it makes any sense..... @templarmc