Plex used to just be a way to manage your local video collection, but that changed a few months ago when support for live TV was launched. At the time, only certain platforms were supported, but now live TV is expanding to Fire TV and the web. For the Fire TV, you also get support for live TV DVR functionality.
You can get a full rundown of how Plex live TV works in our announcement post.
Plex live TV support comes to Fire TV and web interface was written by the awesome team at Android Police.