The Desktop Environment (DE) is an extension of a Window Manager, inasmuch as it greatly extends the base function of drawing and managing application windows. A DE has many other roles, it offers applications that play nicely together, appear the same and often utilise each other. A DE will most probably come with a graphical file manager, a terminal emulator, and some sort of settings manager as a minimum, and most probably with a reusable framework, which allows developers to create components, that integrate into the given environment nicely.
Bigger DEs come with desktop widgets, eye-candy, (like desktop effects, shadows, nice fonts, different window decorations (although this is done by the WM), overall look and feel changes, application menus, system tray, application switchers, notification system, and the list goes on.
When you install Debian, you will be given a choice of DE, that you can have with your system, but you are not limited to have only one. You can install any additional DE, and choose the one you like to use when you log in.