The Windows 'Shadow Copy' aka 'Volume Shadow Copy Servce' does filesystem snapshotting. The Linux equivalent requires changing your filesystem/partitions, or possibly using 3rd party tools.
Options
- LVM -
- you must leave free space on your volume group, and has a pretty high performance cost. All though not super fast it is available, stable, and pretty usable out of the box on most Linux releases.
- btfrs - not entirely stable
- be careful to read the note about setups that should not be used. Apparently it has some major ways it can be broken and result in full data lose.
- zfs - not natively available on most distributions yet.
- Very popular option, but is very difficult to use as a root fs on Linux. Great for data filesystems
- R1Soft Hot Copy - https://www.r1soft.com/free-tool-linux-hot-copy
- I haven't used this, but I don't believe it is designed for long term snapshots, instead it is just used for getting a clean backup.
So, if you need to snapshot your root FS, I suspect you probably need to setup the system with LVM, and leave lots of free space in your volume group.
If you need snapshots for a data-only filesystem, I strongly suggest you look at zfs or maybe btrfs.