Plex allows you to cast videos, photos, and music to your Chromecast device, which you then control from a casting Plex app. Plex also supports content mirroring so that as you browse your content on your device, details for the item are shown on your Chromecast to help create an immersive experience.

It’s important to note that the Chromecast streams content directly from the Plex Media Server. When you use a mobile device or browser to initiate a cast, (unless it is synced content) the content does not go “through” that device and then to the Chromecast; you’re free to disconnect or turn off the casting app at any time if you wish to do so and that won’t affect the stream.
For instance, it’s possible to start the cast with one device, disconnect it, and then connect to the Chromecast later from a completely different device to control the playback.

Related Page: Cast from Android (devices using Google Play Services)
Related Page: Cast from iOS
Related Page: Cast from Browser or Desktop (via Chrome browser)