Can someone explain what this SYSTEM group really means, and what it is for?
The system account and the administrator account (Administrators group) have the same file privileges, but they have different functions.
The system account is used by the operating system and by services that run under Windows. There are many services and processes within Windows that need the capability to log on internally (for example during a Windows installation).
The system account was designed for that purpose; it is an internal account, does not show up in User Manager, cannot be added to any groups, and cannot have user rights assigned to it. On the other hand, the system account does show up on an NTFS volume in File Manager in the Permissions portion of the Security menu.
By default, the system account is granted full control to all files on an NTFS volume. Here the system account has the same functional privileges as the administrator account.
NOTE: Granting either account Administrators group file permissions does not implicitly give permission to the system account. The system account's permissions can be removed from a file but it is not recommended.
Source How the System account is used in Windows