Actually, I don't care whether you talk about filesystems or any other thing that might be Quiesce'd in a software setting. I'm just looking for some more clarification about what this bit of technical jargon actually means.
Have you looked at the wikipedia description:
So it is pausing to get the system in a state that can not only be backed up, but also successful restored. If processes just go on writing you might have the first half of a new file content, but not the second half in your backup.