Android PLEX: What additional functionality do I get for a one-off €5.99?

When I start the Android app from Plex and want to play a video, for example, a pop-up appears offering me a one-off booking of €5.99.

What extended functionality am I buying?

You are buying the ability to play a video for more than 1 minute, if it’s streamed from a personal Plex Media Server (which in your case is probably running on your Synology NAS).
That’s it.
It is NOT a Plex Pass.

https://support.plex.tv/articles/203868088-unlocking-or-activating-plex-for-android/

(There is no playback limitation when streaming videos from the VoD catalog on plex.tv or the TV streaming channels on plex.tv)