The 10 teams that finish in the lower half of the standings have protected first round picks in the following year's draft. The Mets missed this qualification by one loss.
It's also worth noting that if a team drafting lower than 10 signs a Type A free agent, like the Mets, they lose their first-round pick. However, unlike in years past when that pick was transfered to a different team, this year (because of the new CBA) the pick is simply erased and everyone else moves up a slot.
Oct. 4, 11:30 am: According to this post on Deadspin.com, the 11th pick in the draft is cursed.