First, no one is ignoring you and you application materials certainly aren't being thrown out as long as you're applying via USA Jobs and following all of the directions. Getting a Federal job is tough- there's a ton of competition- and it's unrealistic to think you're going to hear back about most (or even many) of the applications you submit. Regarding your specific question, "varied backgrounds" means whatever you want it to as long as you discuss experiences you've had and acknowledge those you haven't had but look forward to in the future. Understanding diversity (experiential, cultural, racial, ethnic, etc.) is a significant component of Federal work and the presence of such diversity makes our workforce strong; it is important that prospective employees recognize and respect this fact and are well-positioned to work with colleagues from a wide variety of backgrounds- it's a big country, and folks from all parts of it work in government. It also looks like the particular role you're interested in may be fairly high profile, so it will likely be critical to demonstrate your ability to communicate effectively. Prior to submission, I recommend sharing your KSA responses with several people; take their (constructive) comments and work to prepare a series of clear, well-written paragraphs. Presentation may be an important part of this application, and this is you opportunity to show how capable you really are.
Hope this helps; good luck!