Docker is a solution for the management of lightweight process containers.
Docker can be installed from Stretch Backport or Jessie Backport repositories (see the docker.io package). Docker upstream also provides packages (for multiple different debian version): https://docs.docker.com/install/linux/docker-ce/debian/
Debian images are available in the docker.io official repository, but you may as well create some yourself (see more details on both options below). In Docker terminology, an image is an object that you can download, and reuse to instantiate new containers.
Ready-made images from docker.io's official Debian repository
Debian images provided in docker.io's official repositories (their "official images") are listed on their official debian images repository. The way these images are generated is now documented quite well in the image description (see below for pointers on re-creating images).
All that it takes to construct a container based on this image, is to use a declaration like the following in a Dockerfile :
However you may not trust their maintainer on having done the right thing for you. See for instance https://joeyh.name/blog/entry/docker_run_debian/
Manual base image creation
See Cloud/CreateDockerImage for a detailed procedure (similar to the one used for the ready-made images), using the classical debootstrap Debian tool.
Of course, you'll then need to name that image in your preferred way, to reuse it in later Dockerfiles, for instance with :
Running services inside Docker containers
See https://www.debian-administration.org/article/698/Automating_the_creation_of_docker_images for a description of how to automate image creation for services running Debian, which describes a way to ensure services will be started properly by runit inside the containers.
You may also be interested in the Debian adaptation of baseimage-docker made by obergix, which also uses runit to control services run inside a container.
John Goerzen has a set of Debian images which feature a full standard init system, cron, SMTP server, etc. in about 11MB of RAM. These are available for jessie, stretch, and sid, and are further discussed in a blog post.