Debian "derivative" is a colloquial term used to refer to distributions which are based on Debian in various ways.
A common, but not unique pattern for derivatives is that of reusing/rebuilding most of the official Debian packages and adding some custom packages of their own.
According to distrowatch, Debian has already spawned more than 120 derivatives.
Derivatives/Census: a census of derivative distributions and their information
DerivativesFrontDesk: where to ask help if you come from a derivative distribution and want to contribute to Debian
Derivatives/Guidelines: guidelines and advice for best practices within derivatives
DEX: Derivatives EXchange; cross-community teamwork
UpstreamGuide: some things to think about when you are creating new software to put into your distribution
DebianPureBlends: a subset of Debian that is configured to support a particular target group out-of-the-box
MergeDerivedDistributions: a proposal for how to bring the work of derived distros into Debian
Debian Live: downstream distros using Debian Live technology
CommercialDebianDistros: commercial Debian distros
Wikipedia: Wikipedia list of Debian based distributions
Debian family tree: graph of the Debian family by Wikipedia contributors
LWN: LWN distribution list, search for Debian to find Debian derived ones
distro timeline: GNU/Linux distro timeline
community poll: Debian community poll that included the question "Are you using Debian derived distributions, too?" and resulted in a list of derivatives people use.
Ubuntu: list of Ubuntu (and therefore Debian) derivatives
Multimedia distros: list of multimedia-related distros that are directly or indirectly derived from Debian
UnofficialRepositories: unofficial repositories
Linux Leaders: Debian and Ubuntu Derivative Distros by Bruce Byfield