There are lots of reasons for starting / maintaining a blog on your website.  The reason you have a website in the first place can usually be applied to justify having a blog.

Give Your Company a Face

People like to talk to (correspond with) people; and the 'personal touch' can help to break down the barriers that prevent the formation of trust.

Help to Establish Your Brand and Get Your Name Out There

If those reading your blog like what they see, they'll be inclined to share your site, your brand, your name with others in their social networks.

Point out Your Uniqueness

Be different, because you are different! The blog is perhaps the best way to "blow your own horn." Use it to focus on why your products and/or services are winners. Be tasteful, but be heard!

Give New and Updated Information

Breaking news, great new products or services, and updates on what was getting 'stale' can all keep folks coming back to read your latest posts. Better yet, when they subscribe to your blog, they receive automatic notifications and are then just a click away from your site.

Connect with Your Followers and Build Relationships

Trust is built up over time. Once people become engaged in your blog content - text and/or photos and/or videos, they tend to return for the latest and greatest. However, if your posts are few and far between, the likelihood of capturing their hearts is slim to none. Be consistent and regular, to the extent possible.

Generate Sales

You can add "meat" to your blog by offering surprise deals or specials that are only made available there. You may want to provide a limited time discount on new items, or perhaps sell off discontinued items to your faithful or new followers.

Search Engine Placement

Stats indicate that websites with blogs get twice as much traffic as do websites without blogs. Your blog content, plus the comments left by visitors, can be set to remain online for months at a time, and search engines use it all to help others to find you!