Earlier quoted context omitted.
I'm afraid answers like this actually make the confusion problem worse (nothing against your comment, just an observation in general.) If you're confused about the differences between similar-sounding products X and Y, the fact that "X runs on Y" or "Y supports X" has never made the situation any better, it only makes the line between X and Y even more blurred. I think this is especially true of Mesos, because people…
"X runs on Y" at least implies Y is "lower level" than X. As I understand it, Mesos is analogous to an operating system kernel for your cluster, while Kubernetes is a CaaS (containers-as-a-service) layer on top.
Kubernetes can also run directly on VMs or physical machines.