A PBN stands for 'Private Blog Network'
The main aim of a PBN is to manipulate the search results, by having a network of websites which all link to your money site. Their objective is to attempt to manipulate Google into thinking the links are legitimate votes, aiding your main site with the benefit.
PBN's can get very complicated, and they certainly do still work if they are done correctly. The problem with having a PBN is, if Google finds them (which they're very good at!) the network will be deindexed, and your money site will also get a penalty which will be pretty difficult to recover from.
The other issue is, as you mention, people sell PBN links. If they sell the links - it kind of takes the 'private' away from 'private blog network'. Therefore footprints are left, and it increases your chances of Google finding the network, and taking it down. Google Penguin: https://en.wikipedia.org/wiki/Google_Penguin was an algorithm update which was brought into play, specifically to find PBNs/dodgy links in general.
Personally, I'd recommend staying clear of anything PBN related. Especially if you want your website to have longevity.