Broadly speaking kubernetes saves time by providing an api for existing Linux technology. For example, iptables, ipvs, storage, self-healing, virtual ips, etc via yaml.
Kubernetes was created to give anyone "Google like, production grade" infrastructure without the vendor lock-in of the cloud. And kubernetes on physical machines is where it shines most.
EDIT: it is very easy to complain that kubernetes is complex, but try to do virtual ips with keepalived, corosync, pacemaker to understand how much time kubernetes saves by providing the same capability in a generic way which is easy to use. I have the feeling that people take kubernetes for granted without knowing how much manual work one has to go through in order to build a similar experience using the standard building blocks available.
EDIT 2: straight out of kubernetes home page: "Kubernetes builds upon 15 years of experience running production workloads at Google" that is a lot of saved time just by using kubernetes.