Essentially, when you use blogging (creating and publishing valuable content), geared toward your target audience, and optimize it with keywords related to your business, it will raise your organic search results allowing those who are likely to be your customers to find you online (this is the inbound part--they're drawn in). Once on your site, if visitors value your content, and you're continually produce more new content regularly (blogs, whitepapers, ebooks, etc.), visitors will hopefully continue to come back to your site and eventually become customers.
It's a great way to build online awareness, generate leads and create a loyal following.
Here's some additional recommended reading on the subject of inbound marketing (affiliate).