It's hard to say--by virtue of the number of applications it gets and its small class size, GSB can be extremely selective and only take very exceptional people. Obviously good grades and GMAT and recommendations will help, but there's a lot more to it as is the case with any top school really.
Stanford seems to want people who have bold post-MBA plans as opposed to people who give the standard consulting/IB/PE answer to their career goals. I submitted essentially the same application/same positioning for both GSB and Haas and got dinged by GSB without an interview, yet accepted by Haas with a scholarship offer--I think my biggest downside on my GSB essays was not making a compelling case for why I needed a Stanford MBA and what kind of spectacular things I would do with it. Haas must have been impressed by what I had done, but Stanford must have been looking for more in terms of what I
would do...that's my take on it anyways.
A few GSB students recommended that I check out this guy's story during my application process as a good example of what GSB wants:
https://www.nuruinternational.org/videos/theendjakesstory.htmlApparently his career goals essay was basically a written version of that video. Pretty powerful stuff.
If you've got a background like his, and a bold, creative plan to beat terrorism by ending world poverty, Stanford is more likely to give you a serious look than if you come in with a vanilla life story and career dreams.