You're basically right about Shadow Copy: when you write changes to a file, Shadow Copy saves the disk blocks from before the change, and so you get the ability to roll back changes via the "Previous Versions" tab on a file or directory's Properties.
Whether or not you want to do that depends, of course, whether you want that feature. If you don't, then it's just a drain on resources (extra disk writes with every change). The "filling up" is going to happen if files get lot of changes, and/or disk space is tight. If you look up the specific error codes at Microsoft Support you may find more info.