We are preparing for the backup strategy. As our repository is very huge nearly 600 GB. What is the best option for backup. Is it online or offiline?
If you can afford downtime, that Offline backup would be the best option.
Detailed information about backup process -> Backup and Restore
But what does the filesystem snapshot. I am no expert in linux. Can we find the documentation on how to take filesystem backup?
Filesystem snapshot is the state of a system at a particular point in time. Offline backup should be taken by someone who is a Linux expert and should be tested by trying to restore it.
If you are not a Linux expert, your best bet is Online backup which requires the least amount of Linux expertise. Check the "AEM Online Backup" at  for more details.
 Backup and Restore