KDE is a comprehensive desktop environment with a huge number of applications written for it and a huge amount of users. It is based on the Qt framework.
There are two versions of KDE. KDE4 is a mature version that combines libraries and the desktop environment into one set of packages and has numerous appplications that can be built on that base. For KDE5, the libraries, now called KDE Frameworks 5 or KF5, are separate from the desktop environment called KDE Plasma 5. Both envionments can be installed, but Plasma is not yet considered stable.
For more information visit the official KDE project site at http://www.kde.org/.