What does Kubernetes actually do?

Kubernetes is billed as a container cluster "scheduler/orchestrator", but I have no idea what this means. After reading the Kubernetes site and (vague) GitHub wiki, the best I can tell is that its somehow figures out what VMs are available/capable of running your Docker container, and then deploys them there. But that is just my guess, and I haven't seen any concrete verbiage in their documentation to support that.

So what is Kubernetes, exactly, and what are some specific problems that it solves?

#kubernetes