In most situations, Plex apps use our Plex Companion functionality to control other apps and fling content from one app to another. In addition to that, though, our iOS and Android apps both support AirPlay to let you play content on an AirPlay device such as AppleTV.
Related Page: Plex Companion
Plex for Android
In Plex for Android, available AirPlay devices will appear in the regular Connect to device window. Just use the normal Players button to open the window and then select the AirPlay device. When you do so, content will be played on the selected device rather than on the Android app itself and you can then use the Android app to control playback.
Note: The support is for full AirPlay devices (such as Apple TV). This does not include what are often advertised as "airplay speakers" but which, in fact, actually use the old AirTunes protocol.
Plex for iOS
To connect to an AirPlay device in the Plex for iOS app, you'll just use the regular iOS Control Center as normal. Swipe up from the bottom of the screen to bring up the Control Center, then select your AirPlay device there. When you do so, content will be played on the selected device rather than on the iOS app itself and you can then use the iOS app to control playback.