What is the difference between Docker Swarm and Kubernetes/Mesophere?

Disclosure: I'm a lead engineer on Kubernetes

Kubernetes is a cluster orchestration system inspired by the container orchestration that runs at Google. Built by many of the same engineers who built that system. It was designed from the ground up to be an environment for building distributed applications from containers. It includes primitives for replication and service discovery as core primitives, where-as such things are added via frameworks in Mesos. The primary goal of Kubernetes is a system for building, running and managing distributed systems.

Swarm is an effort by Docker to extend the existing Docker API to make a cluster of machines look like a single Docker API. Fundamentally, our experience at Google and elsewhere indicates that the node API is insufficient for a cluster API. You can see a bunch of discussion on this here: https://github.com/docker/docker/pull/8859 and here: https://github.com/docker/docker/issues/8781

Swarm is a very simple add-on to Docker. It currently does not provide all the features of Kubernetes. It is currently hard to predict how the ecosystem of these tools will play out, it's possible that Kubernetes will make use of Swarm.