A window manager is a program that just "manages windows". It gives
applications an area on the screen where they can be displayed and most
often the WM draws a border around it, gives it a nice title and enables
the user to do things with these windows - put one on the foreground,
minimize another one etc.
Very often window managers come with some kind of a panel, virtual
desktop support and some kind of application launcher (a "start menu" or
icons on the panel), but strictly speaking, this is exceeding the task
of a minimal WM.
Desktop environments (KDE, Gnome. Xfce) do far more than that. They come
with a file manager, draw the background with pixmaps and icons, they do
some work behind your back to easily handle removable storage or enable
drag'n drop. They come with "control centers" to do system
administration and generally give the user a simplified, cleaned up view
on their system. Applications supporting the DE all look the same and
share a lot of routines to do common tasks. DEs also provide
applications with a way to register themselves for a filetype which they
can handle, which is then reflected when using the DE's file manager and
so on... Of course, this list is not complete.