If there's anything that makes wannabe writers scream in frustration, it's trying to understand just what in the world an author's platform is. This is usually because whenever an agent or editor gets asked, they point to someone like Martha Stewart, whose TV shows, houseware products, and previous books are all part of her platform. Well, great for her, but most of us won't ever have a TV show.
An author's platform is generally defined as whatever avenues the author can use to sell their book. This includes everything from being able to get interviews to being part of a large nonprofit organization with a newsletter. If the author's name is recognizable, that's an instant platform - the name sells itself. This is why celebrities get published all the time.
It's a bit like branding, really. When you want to publish, especially nonfiction, you're going to need to brand yourself and your book. You need to establish credibility - if you're writing a book about dogs for instance, you need to show why you're the right person to write about dogs, why no one knows more about these dogs then you, and why you're an expert in your field. And then you need to show them how you can sell this book, because you can get along with humans, too. The two together, your reputation and how you approach sales, is your brand or platform.
The platform doesn't have to be national to get you published (although, realistically, it's better if it is). To build a platform, or to sell your platform to an agent or editor (you're really selling both your platform and your book when you send in a manuscript), you need to think about what is it you can do to get people's attention. Do you have personal connections in your field that will help promote the book? If you put out a press release, will there be news stories printed about you? Does your opinion even matter to your colleagues?
If not, you've got to find a way to build your platform. In today's technology-based world, it's all about creating your own way. Building an author's platform is all about the website and social media. If you're not someone who has a traditional platform but truly believe you're the person to write that back, go out and get yourself a blog. Aggressively promote yourself on websites that are respected in your field to attract readers (just not to the point of spamming - people hate that). You can create a platform, thanks to the internet, in ways you could never have done before.
And, in reality, this is also true for fiction writers these days. Anything you can do to make yourself visible in the eyes of the marketplace will only help your chances of getting the agents and editors' attention.