There's many different linux distributions (commonly called distros). These are basically different versions of linux, a bit like a whole different operating system. Many distro's are built on other distro's. Some Linux distros include:
A desktop environment manages the desktop. Most of them come bundled with software like word processor (As KWrite in KDE).
KDE is a desktop environment for Linux. KDE stands for the K Desktop Environment.
The gnome desktop is one very widely spread desktop environment. For instance, Ubuntu uses it by default.
Xfce is a minimal desktop environment with minimal hardware requirements.