The K Desktop Environment (KDE) is a free software project which aims to make a complete user-friendly desktop environment. It's dozens and dozens of seperate programs who work together to form a complete desktop environment.
 The libraries
The KDE libraries makes it real simple to write software for KDE, or more correctly, software who require the KDE libraries. You don't have to use KDE to use programs written for KDE, they work just as well in any window manager / desktop environment as long as you have the libraries installed. Also, the different pieces who make up the KDE desktop can be used without running the whole desktop environment. kdesktop, which draws the icons on the root window, can be used as a nice addition to Fluxbox.