The short answer is that you need to be very, very good. There are a lot of terrific, aspiring entrepreneurs out there, and so a bit of luck is useful too. Having said that, winning isn't everything.
buySAFE is actually a product of the 2002 Wharton Business Plan Competition, but the plan was not the winning plan. PayMyBills.com has a similar story. The founders and my good friends, Jeff Grass and John Tedesco, were finalists, but not winners, in the 1999 Wharton Business Plan Competition. However, they went on to raise tens of millions in venture capital and they built a really nice business in the process.
Simply going through the business planning and critique process is the real benefit of these competitions in my opinion. Business plans are funny things. Business planning is a fairly simple exercise, but if you haven't previously developed a plan, the effort can seem very daunting. Business plan competitions typically provide basic advice to the entrepreneurs on how to get started. The competitions also have multiple stages with each stage presenting an opportunity to receive valuable feedback from the experienced entrepreneurs and investors that are judging and/or mentoring in the competition.
The following Business Week video does a nice job of covering the basics regarding what you need to know before submitting your business plan.
In the video, the University of Oregon's Randy Swangard talks about how to win that business plan competition — what to keep in mind before you apply, and why it's sometimes better to come in second.
The Wharton Club of New York is running a business plan competition now, and here is all the information you need to enter as a participant. I highly encourage you to participate if you can.
Also, you might find the following NY Times article interesting. "Beyond Grades: Business Students Put Their Start-up Ideas to the Test" does a nice job of covering the ins and outs of business school business plan competitions.
Have fun, and good luck!