I’m using macOS and the Nextcloud client. If, for example, my disk space is full, would moving data in my Nextcloud help reducing my disk space? Or ist it just synchron?
Sync. If you delete data from the computer, those deletes are replicated (as client is master)
Yes you can free space.
Put your files in your nextcloud folder.
Wait for the sync.
When it’s done open nextcloud client proprietes.
You can uncheck folders that you don’t want to see on your disk but that you still want present on the nextcloud server.
Apply and your folder will vanish from your disk
Edit: nevermind 
It’s the same on Windows.
Alternative: Use directly the webdav storage (directly from your server without local copy). You can mount it with apple+k
Oops uncheck delete. Ignore me.
Oh well I did drag and drop it to my Nextcloud folder and it vanished of my desktop. But all files are stored in the Finder under “user” and there is a Nextcloud folder with a green check mark on it.
So, how to free up like 20 GB of videos? Just move it to my local Nextcloud folder, wait for it to be synchronised and then remove the folder in the Nextcloud settings?
Yes. Absolutly