Usenet is a federated forum system originally designed for text-based discussion, kind of like you're doing here.
At some point, people realized that if they could encode files into text, they could distribute them as a number of messages over Usenet.
A file was typically split and encoded in text format using something yenc.
One limitation of Usenet is that sometimes some messages were dropped. To avoid having one missed message, usually something like PAR was used to add redundancy that could "rebuild" up to a certain number of dropped messages from redundant information.
Usenet software was written to download all of the messages that were part of one "binary" file.
To facilitate this, someone introduced NZB. An NZB file contains a list of messages containing chunks of the file and and associated redundancy that belong to a single file.
While the system was often used to distribute pirated content, it wasn't limited only to that.
Transferring files in this manner is fairly bandwidth-inefficient; a given binary is transferred to all Usenet servers out there (unless they explicitly block binaries), and the practice tended to drive up the costs of running a Usenet server that did not block binaries.
It's...not a peer-to-peer system at a technical level. Peer-to-peer systems involve User A's computer transferring a file to User B's computer. This has a federated system of servers that host content. However, it is somewhat similar to some peer-to-peer filesharing systems that you may have used in that it was often used to transfer pirated content.
It used to be that Usenet service was bundled with Internet service, but as the costs rose and most people didn't use Usenet, various providers tended to drop support. In general, if you want to use Usenet with binaries today, you'll probably need to get a commercial subscription to a provider who sells access to their Usenet server.