When you're in business there's possibly no more valuable information than what other people and companies are saying about you. With social media, since most of the content is in the public data "streams", it's easy to track comments and mentions of your company or your own name.
Why is it important to know what others say about you and your business? You're not just looking for compliments (which are nice to find) but it's also helpful to know if people when complaining about or criticizing. In addition to thanking or maybe returning the favor for someone who praises your company, with knowledge of what's being said you can also do damage control if someone is dissing you.
While you for sure do not want to get into a negative message exchange with anyone on social media, knowing what's being said does give you the chance to state (your version of) the facts.
Social media can also be a great tool for quality control (know what people do and don't like about your business) and customer relations. For example, if someone is happy with your business and says so online, you can thank them publicly - which is a nice thing to do. And if someone has a problem, imagine how powerfully positive it can be if you contact them based on their posting about it on social media and do what you can to make it right?
To an extent, you can also use self-tracking to test the effectiveness of your marketing and advertising in all media, including social media. Because many people Tweet or post about anything they do, have, or buy, tracking mentions of your company during or after a promotion can be a measure of the promotion's impact.
It's pretty easy to do simple tracking. Facebook and Twitter, for example, each have a search feature that makes monitoring mentions of your business, your products, or any of your personnel simple. Depending on the uniqueness of the terms you search on, you may have a lot of results, but built-in filtering can help separate the useful from the irrelevant.
If you're searching on your name, you might find that adding your location will narrow, or at least order the search results. If you have a common name, as I do, you many find another person with the same name in the your town who is mentioned on social media. It can get a little confusing in that case - not for your friends or for customers who know you, perhaps, but possibly for people who are just looking you up or only know you by name and not by your photograph.
I've been fortunate that the other "Bruce Brown"'s in my area are nice guys, but if they weren't or if they were in the news or mentioned on social media for negative reasons, I might not like it, but at least it would be helpful to know what's being said by or about a namesake.
The bottom line is that not only does social media give you the ability to communicate in public, it also provides tools that can help you track your impact and your image.