When using Twitter for a business there are several possible uses.
The most obvious one is for marketing. Most big companies and many smaller companies have taken to using social media sites such as Twitter and Facebook as a cheap method of promoting their products or services. For example, smaller retail stores may reveal a secret code word for an in-store discount. This actually encourages their fans/followers to not only regularly look at their posts but also encourages them to head into the shop.
Most of the world’s corporate news seems to focus on the same dozen companies, especially tech companies such as Microsoft, Google, Apple etc. Any breakthroughs for smaller companies, or even smaller news on smaller companies are easily buried deep within newspapers / easily skipped over online / completely disregarded in general. With your own social media accounts, it is much easier to broadcast your latest news and headlines directly to people who are interested in you.Twitter can also be used as a help desk/hotline for your company.
Searching for mentions of your brand name on twitter can help you understand how your customers perceive you and you may even reply to them. If someone tweets “My *brand* TV just stopped working… never buying from them again” you could reply saying something about your warranty or return policy, or maybe even troubleshoot the problem to find out if it is actually broken.