A nonfiction author's blog can approach the topic from several directions:
New developments.
New products or services.
Hot-button issues of the day.
What other blogs or media are saying.
Reviews of new books in the field.
You can publish a blog in the style of a perpetual newsletter, an aggregation of interesting tidbits about your book's topic. As you notice new things and write about them, each post is stacked on top, and with each new post added on top, one of the older posts is bumped from the bottom and sent to your archives.
Let's imagine you're writing a blog on the topic of Organic Strawberries. Your blog could serve as an information clearinghouse covering every conceivable angle and trend of organic strawberry growing, cooking and consuming. You'll constantly monitor consumer and trade media for the latest news on organic growing, interpret this material for your audience, and link to the source material, adding your own commentary.
Your blog could include:
Questions from your blog readers on organic fruit, along with your answers.
Guest articles from experts on organic strawberry gardening.
New books and magazines on the topic.
Strawberry dessert recipes.
The best places to grow organic strawberries.
Listings and maps of markets offering organic strawberries.
Reviews of cookbooks addressing natural, organic, fruit and dessert preparation.
Fiction authors have even more freedom, but a bigger creative burden. They can write about themselves, or even from the point of view of a fictional character. A story from their book can continue on the blog, veering off in new directions, experimentally, in response to suggestions from readers and other writers.