Docker is used as an application container runtime. The main usage is for running containers (as a task) on top of Mesos via a Mesos framework.
For example the Marathon and Kubernetes can both utilise Docker to deploy, manage and run containers.
For more information on Docker see https://www.docker.com
The reason behind choosing Docker is it allows clear separation between the application/task and the underlying operating system. As such this gives developers full flexibility about what they choose to run on top of Apollo.
We use Docker in combination with Weave, with weave providing the virtual networking layer which makes accessing Docker containers across multiple hosts simpler.