The Plex Media Server is installed on the main drive of your Mac – same as the OS and your other applications. Same goes for all of Plex’ configurations and metadata / posters.
If you have no backup, you’ll need to reinstall Plex and start over.
https://www.plex.tv/media-server-downloads/
Edit: what’s so bad about your internal drive that you want to move the app and its data to an external drive? I’m not quite sure what positive effect you’re aiming for 
As for moving the data directory you can check out a related post:
