The ARR tools are basically a search engine website you host. The interact with a few other tools you have to have access to/pay for. Namely an indexing service and a (for some) a download service. They can use torrents, so you dont HAVE to pay for downloading, but using something like newsgroups is really nice and add reliability and security.
THe “ARR’s” basically then are just a fancy UI and scheduler and just search the indexing service, download the files you want, re-assemble them and copy them to the location you want (often a file share that your media player like Plex or Jellyfin will use).
You can set them to continually look for something too. So for Sonarr, it will auto-download new episodes as soon as they appear in the index. Or if you see a commercial for something upcoming, you can add it and monitor it and as soon as it starts showing up in the indexes it will download.