Any VPS offers block storage as that’s the only way your VM can see a virtual disk that it can format and partition and what-not. The backend storage in KVM could be a local LVM pool, or it could be a LUN to a SAN (or LVM on top of the LUN). You don’t need to think too much about this, that’s the provider’s problem (although if you’re looking for performance, it’s important how they define “local” storage).
As far as you / your VM is concerned, you can use LVM to enhance your own experience, e.g. your VM comes with default 40GB SSD for the OS and 500GB of additional storage (call it a 2nd drive), the latter of which you get over 80% utilization after a year and you request for more storage. Now you have 1TB of space on the 2nd drive, but your partitions inside the VM are still only seeing 500GB, despite your drive now being 1TB. You can use LVM to expand the physical volume (pv) to the max size of the disk (to 1TB), then the volume group (vg) will see that change and now you have 500GB of available space in the volume group (unallocated) and another 500GB (the previous one) allocated to different logical volumes (lv).
You can then allocate more space from the VG to any of the LVs on the fly, live, without interrupting your services. Had you not used LVM, you would need to stop your programs running from the 2nd disk partition’s mount path, unmount the path, expand the partition (with fdisk / parted / gparted) and do a file system expansion too (resize2fs or xfs_growfs), mount the now larger volume then start your programs again.
If you use a VPS from a provider that uses old technology, they might not be able to even expand the 2nd disk to 1TB, only give you a 3rd disk of 500GB in size. Then if you didn’t use LVM, you don’t have a way to grow your previous mount volume. You can partition your 3rd disk, then use LVM to create a new PV on the new 3rd disk partition 1, allocate that PV to your previous VG and now you have the ability like above to grow your old mount point. That wouldn’t be possible with straight out formatting your vdisks directly.
As I mentioned before, LVM also offers you snapshot capabilities (but you need free space left in the volume group, left unallocated). So you can realistically recover your own VM to a previous snapshot if say an update borks the OS.
While you can combine the 40 GB with 500GB using LVM, I wouldn’t do that unless you know exactly what’s the storage tier for each (e.g. if the 500GB is just HDD, I’d keep that separate from the 40GB and only use that 40GB for the OS and the 500GB for a bulk storage, let’s say for a mysql database data folder, like /var/lib/mysql).