So there's the "official" set of tools from servarr.com, but there's a few "unofficial" tools as well, but they all function similarly in that they glue several things together to make workflows nicer.

1. A downloader (either a Bittorrent client or Usenet, but I will focus on Bittorrent).
2. An Indexer, some remote site (like thepiratebay.org) or BitMagnet (local DHT scraper) for searching for torrents. Prowlarr is the generic indexer component, so it can provide Indexer's to other components (Sonarr, Radarr, etc.), but you don't need to use Prowlarr if the site
3. A downloads folder.
4. A media library folder.

After adding your media library so the component knows what you "have" already, you tell the component (say "Sonarr" for TV shows) what you "want" and it's added to a wanted list. It also knows what you already have. When you add a new show to your wanted list it can immediately download it, or it can wait for new episodes to be released and only download those. When downloading it will download to the downloads folder and then copy (you can change settings so it uses hard links, so these copies don't take up extra space). It will only copy the media files and ignore .nfo/readme.txt style files, and it will change the format to the one Plex/JellyFin want (with //S__E__ - Episode title.mkv) By default it will seed for a certain amount and then delete the files from the downloads folder/remove from the torrent client, but this is configurable. It can also look for higher quality versions like if you have 480p versions of a show and 1080p versions become available it can download them and replace the lower quality versions with higher quality (it does not do this by default).

But that's fundamentally how they work, they have a media library with certain things, and a list of things you "want" and then a way to download things to get from the want list into the media library without needing to do any manual intervention (except manually adding things to your wanted list)