No not the Kentucky Department of Education. KDE the desktop.
KDE started in 1996 and was developed by Matthias Ettrich. Back in 1996 applications for UNIX all looked different. Matthias wanted to change this and thus, KDE was born. KDE was not only going to be a set of applications with the same look, it would be a desktop environment.
What's in a name? KDE was intended to be a word play on CDE which was developed by HP, IBM and SUN when they founded X/Open. KDE stands for K Desktop Environment. The K was almost decided to stand for Kool, how ever after a bit of deliberation it was decided that the K will stand for nothing. KDE uses the Qt toolkit, an application framework that makes developing applications for KDE a lot easier.
In 2009 KDE transitioned to Mac and Windows as well because of popular applications like Ktorrent, Amarok and others. So it was decided that KDE couldn't be an acronym any more, as KDE was now more than just a desktop.