It seems like they accept based on a wide-verity of factors that may be different for each candidate.
For example read legallyblonde33's post on the first page of last year's thread: Summer Science Program (SSP) 2011
He/she could be being overly humble, but it seems as though they do put a lot of emphasis on the essays. Reading through last year's thread hinted at what legallyblonde33 outright said, which was that the essays were very important.
I think several other previous attendees wrote a little about themselves on that thread, you might want to read through it (but not all at once: that thing is huge!)