A footprint is a recognisable pattern of behaviour that can be traced to a single source. For example if all your PBN sites use the same WordPress template, its a footprint. If all your sites have the same host its a footprint. If all the domains are registered from the same domain seller under the same name its a footprint. We are all guessing what statistics Google uses as a footprint. What Google does is collect all the footprints and they do a statistical analysis to determine how likely the footprint is likely to occur randomly/naturally on the internet. They may have a test where if its say less than 5% chance of the footprints occurring naturally they do a manual review. All this is done by computer until the manual review where an actual person inspects the sites.
The manual review is where all these PBNs get busted except the high quality ones which are built like real money sites. PBN builders take so many shortcuts, it is so obvious even to myself who only started reading on Blackhat SEO for 2 months, that these sites are junk and ought to be deindexed. I have purchased blog posts from various sellers here in the market place. None will pass a manual review. I am just hoping they don't get manually reviewed or I have wasted my money.
The only way to get around this is to build your own PBN and make them look like real sites which do not fall foul of the Google webmaster guidelines. This is expensive though so you do a risk/benefit analysis to decide which route to go.