Now an entirely different issue is if you have any value in keeping your business plan a secret? Most people in business and in Silicon Valley will agree that ideas are cheap and come about often, and it is mostly all about execution.
To that end, I believe that you gain little by keeping your business idea secret, unless you want to be a cool kid and have the lamers at techcrunch or whatever has replaced them with do a big splash.
I believe your best bet is to talk with folks about what you're doing, pitch potential customers and investors and competitors equally, and don't be worried about keeping anything secret.
The counter to this, is that you want your messaging to be clear. If your message is too broad, and you tell too many people too many different things, they'll dismiss you as unclear.
And as a startup you will be unclear. So only share what you're doing with folks you trust, but not because you fear competitors will steal your idea, but because you only get one chance to make a first impression, so be careful how you use that one chance.
Their reasons are that by not sharing your business assumptions with anybody (especially potential customers/users), then you're violating the fundamental principle of Customer Development and Lean Startup by cutting yourself off from early and valuable feedback which you could be using to rapidly iterate better versions of your product. In other words, you'll be secretive, but (probably) slow and operating completely in the dark, often to your detriment.[1]
However, you may be confusing instead the need to keep secret your long-term plans for world domination if you read/listen to Peter Thiel's CS183 Startup class notes[2] (kindly provided in essay form by Blake Masters), which espouses that coveting instances of certain classes of secrets help drive startups to success. I can't do the essay justice, so I highly suggest reading it to get a better answer to your question.
[1] Search for those terms - they are highly SEO'd
[2] http://blakemasters.tumblr.com/post/22866240816/peter-thiels...
If you are talking about the fundamental mechanisms of how the thing actually works, then that is a different matter.
No company on earth will want to tell everyone how they do it, but they are happy to tell everyone what business they are in. The "how" is not the business plan.