When a blog is linked to your overall business website, it helps to provide fresh content which is something that helps you with search engines finding you and ranking your website. At least that's how I understand it.
Also, when a blog is linked to your domain/website, then the person viewing it doesn't "leave" your site when going to your blog and can easily navigate back to your business site. If you have a blog that is not part of your business website/domain, then viewer ends up leaving your site, which should be avoided when possible. My blog doesn't have a separate name. It's just like another page in my site, i.e.
www.jkvirtualoffice.com/blog
I have seen, however, several VA sites where the blog is separate and a link to the blog is provided on their main site.