I've used Kubernetes for a few years now, and there was a description that really resonated with me: You can think of k8s as an operating system where we can deploy applications, especially those that run more than a handful of services.
Said another way, if Linux (or whatever) is the OS for your server / VM / host level / network device, k8s is the OS for your cloud application.
And, when k8s is implemented properly, it takes a lot of headaches that can come from dealing with the myriad problems that arise when your architecture goes beyond a basic handful of "tiers."