It's not one of our major channels, but we do post a few times a day (mostly scheduled posts using Hootsuite) and we do see traffic to our main website and our blog from there. It's taken us years to build up to our current level, though, so no one should expect Twitter to "skyrocket" their traffic overnight.
As to "getting business" from it -- I don't think Twitter is good for driving direct sales or for lead-generation by itself; it's more useful for people toward the upper end of the funnel. In other words, it's more for making people aware of you in the first place, and for helping establish yourself as an expert, maybe driving some initial traffic to your site. Depending on what software you're using and how good it is at tracking multi-channel attribution, you may or may not see Twitter contributing, but if you post interesting stuff regularly, it should be able to send you some traffic, some of which may eventually convert.
When you post links to blog posts or pages on your website, using a link-shortening service like Bitly will allow you to see which specific types of articles get the most click through. That way you can tailor what you post on Twitter to what most interests your audience.
It's also a great customer service channel, if you have someone available to monitor and respond quickly to customer inquiries.
(And once you have a following, it can be useful for sending out quick "breaking news" alerts, such as when your phone system is down or your website has gone offline.)
So, yeah, it has a use for us, but directly driving business isn't our goal in using Twitter.