By utilizing a regularly updated blog for your website, it gives you an opportunity to use search terms that you are targeting, as well as giving the search engines extra content to crawl. A blog gives your site an opportunity to become relevant for those terms you are targeting and provides more content to signal the search engines about what your site is about.
In addition, the search engines value fresh, regularly updated content. Updating your blog regularly gives the search engine spiders reason to crawl your site more frequently. This allows your site to appear to be more valuable in the search engine's eyes, and as a result rank higher.
Beyond the direct SEO benefits, there are some other benefits. Blogging allows you to create a unique voice for your brand, an opportunity for you to brand your company, which will benefit your site's user experience as well as your customer's loyalty. It gives you an opportunity to provide your customer's insight about your company, your products as well as your unique value proposition. Be interesting enough, and others may link back to your posts, which of course will benefit your SEO efforts.