"System file, or folder containing system files" icon next to a folder in the File Manager
If you see an icon with a tooltip "System file, or folder containing system files." next to a folder in the File Manager, this means that the folder, or any of its subfolders down the tree, contain a system file.
System files are usually created by tools of your hosting Control Panel, or by administrative tools on the server.
An example of such tool is the FTP Protection section. When altering the behaviour of any of your FTP subusers through the FTP Protection section, the system creates an .ftpaccess file in the home folder of the subuser. If for any reason this .ftpaccess file is removed, then the behaviour of the FTP subuser will return to the default settings.
You should remove system files carefully and considering the possible consequences.