The sandbox is loosely defined at best and not largely agreed upon by SEOs.
What it generally refers to is that Google does not trust new websites, and therefore places them in the 'sandbox' and lowers their rankings until trust is established (age being a big factor in that trust.
This is because thousands of new websites appear online everyday and only a very small amount are genuine, decent quality and last for the long term, so Google improves its index by punishing new sites.
Whether an actual 'sandbox' exists, or whether it just takes time for a new site to develop trust with Google (or whether both of those are the exact same thing) is open to debate.
Having launched a number of sites and grown them to 6 figure traffic, worked with many other site owners closely who have launched successful sites, and watched the growth of a number of sites I can tell you this...
Google HATES new sites, with the exception of the homepage of keyword domains, getting new sites to rank highly is exceptionally difficult compared to an aged and trusted site. I find this lasts anywhere between 6 months and 2 years depending how well you promote your site, and the number of genuine editorial citations from authority sites. I find that as time goes on and your site grows your Google traffic and rankings will improve considerably if promoted correctly.
That's not to say you can't get good rankings and traffic in the short term, just that it does not compare to what you can achieve with an aged trusted site.
Please jump in with your own experiences and conclusions about new domains, rankings & the Google sandbox.