If you're asking how a blog can help a site's ranking, it helps when it has relevant and search engine optimized blog posts and content. When page crawlers "crawl" your page they will read the content and decide how it ranks in search engine results. Like if you offer a lot of good and SEO'd information on a blog about pastry baking then the crawlers will rank your site higher on the search results than a pastry baking blog with low quality content.
If you have blog with quality content on it, then placing url with anchor text you're trying to rank another of your sites will be very beneficial.
All of the above are reasons that a blog will help you with your site rankings, as long as the content is of high quality. You also need to be sure you use the proper on-page SEO techniques. Another reason a blog could help is it sparks user interaction. Your guests can leave comments and tell you what they think, this is invaluable information!