What is "Backup Manager"?
The better question would probably be: what is "Google Backup". But to that part we unfortunately lack a corresponding user-documentation. All there seems to be is the Backup API reference for developers.
It doesn't look much better with
bmgr either, where there's again a dedicated API reference. What we can read from it is:
bmgr is a command-line programm to be used via adb (
adb shell), which can be used to trigger backups/restores for apps which are installed on the device and support the Google Backup API.