what is meant by a writer's "marketing platform"?

Whatever existing contacts, exposure, or connections, reputation etc., the writer has that aids the securing of purchasers.

Can this also be your background--what makes you an expert on your subject?

What do you plan to do, and how, to help promote and markey your book?

A platform is an established "fan" base of people who are going to buy your book because YOU wrote it. If you're a professor and the book will be mandatory reading in 3 of your classes each semester, that's part of a platform of established sales. If you run a blog with 200 follower, it's not something to mention because it's too small. If you run a blog with 20,000 followers, that would be good for your platform.
Are you a radio personality who can hawk your book on the air and who people will read because you're the awesome DJ?
It's not really a marketing plan, it's more about YOU and people who will read your book because of YOU.