What a PBN means
The name sounds harmless. There is nothing illegitimate about a private blog, and nothing wrong with running several websites either. What turns a group of domains into a network of this kind is the intent behind its existence: the sites are not published to win readers of their own, but to send links to one main website.
The line between this and a legitimate group of websites lies in whether each property has a reason to exist on its own. A company with a shop, a corporate blog and a careers portal runs three sites with different audiences, content and goals; the links between them describe a real relationship and can be explained out loud. A publishing house with several titles works the same way. In a PBN it is the other way round: without the destination site, none of the properties would have an audience or a commercial purpose.
Google does not use the acronym PBN in its policies, but it does describe the behaviour. Its link spam policy prohibits creating links whose primary purpose is to manipulate rankings, and it expressly includes creating low-value content for the purpose of manipulating linking and ranking signals. A private blog network fits that description whatever trade name it is sold under, whether as authority links, content seeding, digital press or an owned media network.