A. VSS consists of several components, including VSS writers that are provided by application authors to enable a consistent backup to be taken of application and OS data without stopping the application or OS. These backups work by making a VSS request. The VSS writers are notified of an imminent backup, so they make sure data is flushed to disk and further activity is cached, ensuring the data on disk that's being backed up is in a consistent state and is restorable.
Hyper-V extends this backup functionality by allowing a VSS backup to be taken at the Hyper-V host level. The VSS request is actually passed through the integration services to the OS of Windows VMs, which then notifies the registered VSS writers in the VM of the backup. So backups can be initiated at the Hyper-V host level and VM backups will still be consistent and usable, without actually doing anything in the guest OS.
Certain versions of Linux are also supported on Hyper-V, but Linux OSs don't support VSS. So a backup taken on the Hyper-V host can't tell the Linux OS in a guest VM to put itself in a backup-consistent state. To back up a Linux OS, either stop the VM while you take the backup or, if you can't have downtime, perform the backup from within the Linux VM instead of at the Hyper-V host level.