If your website is important to your business, then having a blog is important to your business!
If a website is important to a business at all, simply leaving it up with static content is, in most cases, not going to get much traffic. Of course, as long as the people who need it find it, then most people wouldn't mind if no one else surfed to their web pages. So why should it matter?
It matters because whether a website appears prominently on a search engine mostly depends on the amount of traffic going to the site. In order to ensure the right people find a site it helps to get everyone possible moving to it. To reach the people you want to reach, you need to be generally interesting.
To use the common terminology, dynamic websites are going to get more visits than static websites. Blogs ("web logs") are ways in which websites constantly present new content.
Blogging promises you that something will be new the next time you visit.