Change is a good thing. Unfortunately, when you are making big changes to your site or application, there is always room for error. Live-state snapshots takes the idea of a "backup" and brings it forward to its next logical step. Taking a snapshot of your partition not only creates a backup of your files, but also all of the processes running in the background at that instant in time. This way, if you make an error or break something while making updates, you can revert your partition to that exact snapshot, providing a working, fail-safe rollback.
A VPS runs its own copy of an operating system (OS), and customers may have superuser-level access to that operating system instance, so they can install almost any software that runs on that OS. For many purposes they are functionally equivalent to a dedicated physical server, and being software-defined, are able to be much more easily created and configured. They are priced much lower than an equivalent physical server. However, as they share the underlying physical hardware with other VPSes, performance may be lower, depending on the workload of any other executing virtual machines.