Key Concept: Container Pod
While Docker itself works with individual containers, Kubernetes works with a pod. A pod is a group of containers that are scheduled onto the same physical node. In addition to defining the containers that run in the pod, the containers in the pod all use the same network namespace/IP and define a set of storage volumes. Ports are also mapped on a per-pod basis. The Kubernetes Node
The Kubernetes node has the services necessary to run Docker containers and be managed from the master systems.
The Kubernetes node design is an extension of the Container-optimized Google Compute Engine image. Over time the plan is for these images/nodes to merge and be the same thing used in different ways. It has the services necessary to run Docker containers and be managed from the master systems.
Each node runs Docker, of course. Docker takes care of the details of downloading images and running containers.