I should also point out that some modern filesystems like btrfs and zfs have these capabilities built into the filesystems natively so adding LVM into the mix there wouldn't add anything and could, in fact, cause headaches.

In practice, you would split a disk up to keep /home separate from/ and probably other parts of the filesystem too like /var/log.. this has long been an accepted practice to keep a full disk from bringing something production offline completely and/or complicating the recovery process. Now, you could use partitions but once those are set, it's hard to rearrange them without dumping all the data and restoring it under the new tables. LVM stands for Logical Volume Manager and puts an abstraction layer between the filesystems and the partitions (or whole disk if you are into that). This means you can add Disks arbitrarily in the future and add parts of those disks to the filesystems as required. This can really minimize or even eliminate downtime when you have a filesystem getting filled up and there's nothing you can easily remove (like a database).

It's good to know but with the proliferation of cloud and virtual disks it's just easier on those systems to leave off LVM and just keep the filesystems on their own virtual disks and grow the disk as required. It is invaluable when running important production systems on bare metal servers even today.

Hope this helps.