PBN is several dozen or even hundreds of satellite sites that are created to promote the main project in SEO. From these satellites they put links to the main site, thereby transferring weight, which gives an increase in positions and trust to the recipient site. Of course, this is prohibited by search engines because it is a deception of their algorithm and manipulation of search results. And the same Google is actively fighting this: it searches for and blocks networks.
Private blog network - rather a historical name, because at the dawn of SEO, this method of promotion was based on the creation of blogs (usually free ones on LiveJournal, Blogger, etc.) and placing links to your main project on them. But, like all others, this method of weight transfer was identified by Google and the effectiveness of links from such blogs, especially if there are many links, began to tend to 0.
Then webmasters began to hide their donors more sophisticatedly, mimicking ordinary sites. Sometimes it is really impossible to distinguish a PBN site from an ordinary information or news resource.
SEO is not an axiom, but a set of experience and experiments. And PBN is not a panacea, but one of the tools. We rarely get more than 30% of the entire link mass with PBN (usually it is up to 20%). But the choice is yours.
The secret of PBN popularity is simple - it really works! Why not just buy links somewhere? You will find the answer here.