The major benefit of blogging is that it's a great way to establish your authority. By persistently adding informative, useful content related to your niche you can prove beyond any doubt to anyone reading it that you really know what you're talking about; that you're an expert in your field.
This is a good thing in itself, of course. But It's extremely useful if you're in business. It will garner respect and trust from people who you may end up forming partnerships with. And your authority will build confidence in your products and services, thereby increasing the odds that people will buy them.
Then there's blogging's power as a traffic generator. Firstly, it increase the odds that your website, and thereby your business, will be found by people using search engines.
Remember that Google ranks pages separately. And every blog post is another page. So every time you write one you have another chance of ranking for a query (usually a "long tail" search that is highly specific and often contains several words).
It's kind of like fishing for readers. You think about where they might be biting, and you cast your blog line over there. Sometimes you get bites, sometimes not. But if you keep at it you will slowly but surely build traffic.
Say that after several months of blogging you have dozens of posts up there. Of those, you end up with 15 blog posts being found in long tail searches twice a week on average. So that's another 30 hits a week that keep on clicking over.
Now some of those people are sure to click through to the sales pages of your site. Perhaps only a few of these visits result in sales. Maybe none of them do directly. Still, that's an extra thirty people who have found you who wouldn't have otherwise. That has to be a good thing for your business.
As well as the search engine clicks blogging generates all that extra, relevant and unique content under your domain looks good to Google in a general sense. Now, as with so many things related to the search giant it's hard to know just how much influence blog posts have on the rankings of other pages. But they do seem to help, particularly if you link back to them from the blog post. (Interlinking within your own website has long been known to help with website SEO.)
Also, a blog supplies a pounding pulse. You're saying to Google: "Look, my website is alive and kicking. See, I'm constantly adding stuff!" Now if you are competing with someone who's been beating you for various keyword searches but hasn't updated their site for ages this could be just the factor to lift you above them in some results.
Blogging also supplies you with other earning possibilities. You can put affiliate products on your site, for example. You can also rewrite your content and create an ebook out of it, and sell it off the blog itself. (If you are to do this, you should condense and improve it so that it's distinct from the blog itself, of course. That way you won't be charging for something that your readers can already get for free.)
Another reason to blog is that it keeps giving you something new to share on social networks. Sure, you can engage with your followings in a different way, conversing with them and sharing stuff written by others. But it's way more impressive to them if it's your stuff your sharing.
Finally, regular blogging is invaluable if you intend to write for a big media outlet. It might help you get the gig in the first place, and the fact that you've been cranking out heaps of quality content means that you'll be well prepared to do so for someone else.