I can duplicate a service I'm running 1:1 with a new version for testing in 2 minutes, I can tear it down in 2 seconds. I can roll back changes in one command, I can wipe the server and reinstall everything from scratch in 25 minutes.
The environment is completely reproducible, and I can with a single command see every config that applies to a service.
All the usual deployment trouble is gone, no more weird setups and config situations. All the weirdness is nicely encapsulated.
Mainly because the point is non-technical; while I'm not sure that Google is exactly a saintly organization, things like the Summer of Code and giving K8s away have procured some goodwill for them.
The whole article is over the head of Joe User (me) who is competent to use Docker but nowhere near deep enough to contribute code to it.
Kubernetes is like an operating system, Docker is like a format for the executable files.
There is no problem with servers. We're running Kubernetes in production on a single Linux machine, essentially using Kubernetes as an alternative OS.