Debian is an operating system which is composed primarily of free and open-source software, most of which is under the GNU General Public License, and developed by a group of individuals known as the Debian project. Debian is one of the most popular Linux distributions for personal computers and network servers, and has been used as a base for several other Linux distributions.
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The debian:latest tag will always point the latest stable release (which is, at the time of this writing, debian:jessie). Stable releases are also tagged with their version (ie, debian:8 is an alias for debian:jessie, debian:7 is an alias for debian:wheezy, etc).
The rolling tags (debian:stable, debian:testing, etc) use the rolling suite names in their /etc/apt/sources.list file (ie, deb http://deb.debian.org/debian testing main).
The mirror of choice for these images is the deb.debian.org CDN pointer/redirector so that it's as reliable as possible for the largest subset of users (and is also the default mirror for debootstrap as of 2016-10-20). See the deb.debian.org homepage for more information.
If you find yourself needing a Debian release which is EOL (and thus only available from archive.debian.org), you should check out the debian/eol image, which includes tags for Debian releases as far back as Potato (Debian 2.2), the first release to fully utilize APT.
Given that it is a faithful "minbase" install of Debian, this image only includes the C, C.UTF-8, and POSIX locales by default. For most uses requiring a UTF-8 locale, C.UTF-8 is likely sufficient (-e LANG=C.UTF-8 or ENV LANG C.UTF-8).
For uses where that is not sufficient, other locales can be installed/generated via the locales package. PostgreSQL has a good example of doing so, copied below:
RUN apt-get update && apt-get install -y locales && rm -rf /var/lib/apt/lists/* \
&& localedef -i en_US -c -f UTF-8 -A /usr/share/locale/locale.alias en_US.UTF-8
ENV LANG en_US.utf8
<suite>-slim variantsThese tags are an experiment in providing a slimmer base (removing some extra files that are normally not necessary within containers, such as man pages and documentation), and are definitely subject to change.
See the discussion in tianon/docker-brew-debian#48 for some notes/details regarding the specifics of the implementation.
If you are curious about what goes into creating this image, please see contrib/mkimage.sh in github.com/docker/docker (and contrib/mkimage/debootstrap in the same repo). Those are invoked by update.sh in the image repository, which provides some additional functionality such as generating <suite>-backports contents and repacking the generated tarballs for the <suite>-slim variants.
Additional interesting information is provided in files on the relevant dist branch of the image repository, namely the exact command used to build (SUITE/build-command.txt), a full log of the build itself (SUITE/build.log), and the "build manifest" (SUITE/build.manifest, which lists the version numbers of all the packages included in the rootfs tarball).