Restartable mode (/Z) has to do with a partially-copied file. With this option, should the copy be interrupted while any particular file is partially copied, the next execution of robocopy can pick up where it left off rather than re-copying the entire file.
That option could be useful when copying very large files over a potentially unstable connection.
Backup mode (/B) has to do with how robocopy reads files from the source system. It allows the copying of files on which you might otherwise get an access denied error on either the file itself or while trying to copy the file's attributes/permissions. You do need to be running in an Administrator context or otherwise have backup rights to use this flag.