There are a number of distributions based on Debian. Some users might want to take a look at these distributions in addition to the official Debian releases.
Debian welcomes and encourages organisations that want to develop new distributions based on Debian. In the spirit of Debian's social contract, we hope derivatives will contribute their work to Debian and upstream projects, so that everyone can benefit from their improvements.
Why derive from Debian?
It can be faster to modify an existing distribution like Debian than starting from scratch since a packaging format, repositories, base packages and other things are specified and usable. A lot of software is packaged so there is no need to spend time packaging most things. This allows derivatives to focus on the needs of a specific audience.
The Debian community and people from derivatives are available and willing to help guide new distributions in their work.
Derivatives are created for a number of reasons (better localization support, specific hardware support, simplified installation,etc.).
How to derive from Debian?
Derivatives can use parts of Debian's infrastructure if needed (like repositories). Derivatives should change references to Debian (like the logo, name, etc.) and to Debian services (like the website and BTS).
If the goal is to define a set of packages to install, creating a Debian blend could be an interesting way to do that within Debian.