Typically, a business will use a blog to help the business's website rank on search engines. You can absolutely employ SEO tactics, or use paid ads, to help your company homepage rank on page one of Google -- but a more effective, long-term solution is blogging.
To consider how your company can rank on search engines via a blog, we'll start with an example -- let's say you work for a web design start-up with very little online presence.
You decide to spend the first year writing and posting regular blog content that strongly relates to web design. Over time, your traffic increases and other companies link to your site for information regarding web design. When this happens, Google recognizes your company as a legitimate source for web design information. Eventually (with a lot of trial and error), your blog posts begin ranking on page one of Google for terms like "web design", "website builder", and "e-commerce website".
Then, one day, you search "web design companies in X city" and find your company is now on page one. This is likely due, in large part, to your consistent blogging efforts.
Take a look at How HubSpot Uses Blogging to Rank #1 on Google to learn more about specific strategies you can implement to rank on search engines.