Backports are recompiled packages from testing (mostly) and unstable (in a few cases only, e.g. security updates) in a stable environment so that they will run without new libraries (whenever it is possible) on a Debian stable distribution
Backports cannot be tested as extensively as Debian stable, and backports are provided on an as-is basis, with risk of incompatibilities with other components in Debian stable. Use with care!
It is therefore recommended to select single backported packages that fit your needs, and not use all available backports.
For wheezy add this line
deb http://ftp.debian.org/debian wheezy-backports mainto your sources.list (or add a new file with the ".list" extension to /etc/apt/sources.list.d/) You can also find a list of other mirrors at https://www.debian.org/mirror/list
For jessie add this line
deb http://ftp.debian.org/debian jessie-backports mainto your sources.list (or add a new file with the ".list" extension to /etc/apt/sources.list.d/) You can also find a list of other mirrors at https://www.debian.org/mirror/list
Run apt-get update
All backports are deactivated by default (i.e. the packages are pinned to 100 by using ButAutomaticUpgrades: yes in the Release files. If you want to install something from backports run:
apt-get -t jessie-backports install "package"
of course you can use aptitude as well:
aptitude -t jessie-backports install "package"
To guarantee a clean upgrade path from a previously stable distribution to the next stable it is not allowed to upload packages from the current testing to that backport distribution. To allow some newer packages for those systems we create so called sloppy distributions. For oldstable (wheezy) packages from the current testing (stretch) are allowed to be uploaded to wheezy-backports-sloppy.
You can use it exactly as the current backports distribution, just add another line to your sources.list and install new packages via apt-get -t wheezy-backports-sloppy install or apt-get -t jessie-backports install
If you want to get announcements about security updates on backports.debian.org subscribe to the debian-backports-announce mailing list.
Please report bugs that you found in the packages to the backports mailing list and NOT to the Debian BTS!