The primary use case of Plex is to allow you to view and listen to your own media files: movies, tv shows, music. If you have a lot of those types of media files, then Plex is very useful. It can do a few other things, like let you view your photos and watch some free movies/tv offered through Plex the company, but I don’t think the majority of those who run Plex really care about those.
The short version is that you install Plex, point it at your media files, let it index those files and download all the metadata (cover pictures, actors, etc.), and then watch. Plex has apps for most media players these days, including Chromecast. You would install the Plex app on your Chromecast, log into your Plex account/server from the app, and then you’ll be able to browse and consume your own media files. You do need to buy a Plex Pass to consume your content from a mobile device.
To use it from your office, as long as your company isn’t blocking it on the network, then you would just log in through the browser and consume your media files that way. One thing to recommend Plex over Jellyfin or Emby for the relative newbie is that Plex handles the authentication and relaying of traffic between your server, so if you’re not comfortable setting up a reverse proxy or VPN to access things on your server from the outside world, Plex handles that for you.
If you have any more questions I’ll do my best to provide helpful answers.
For me, it’s a replacement for Feedly. I use a browser to access it on desktop and FocusReader on mobile. I like to own my data as much as possible.