Both the client and server connect to plex.tv which then brokers the connection between them. They essentially work as a very limited vpn between your clients and server.
This also gives them unrestricted access to the entirety of data passed between devices; and the ability to request any and all info from your server to be handed to whoever they chose.
This is also how they allow you to 'share' content/libraries with each others servers; through their public infrastructure that's collecting your information. Information they then sell to third parties to support their development and broker content agreements.