A Microsoft file hosting and synchronization service.
Turning off the Pictures folder sync in Manage Backup changes the default save location for new pictures from OneDrive (C:\Users\username\OneDrive\Pictures) to your computer (C:\Users\username\Pictures). It does not automatically move the existing pictures stored in OneDrive. You must move them yourself. But since OneDrive is still syncing, any files you remove from the OneDrive folder will be removed online as well.
If you want to keep your files online-only, keep them in the OneDrive folder, but right-click them and select "Free up space".
See this video about Files On-Demand: https://www.youtube.com/watch?v=UzIA9uykIhE&t=43s
To restore all your files, go to the online recycle bin at onedrive.com. Scroll down to the last file in the list. Hold down the Shift key and select the last file in the list. Now all files should be ticked. Click "Restore" at the top.