What is a desktop?
The term desktop refers to the graphical environment where you do your work. The desktop usually consists of a workspace (called the root window) with pretty icons and quite possibly a menu that pops up when you click on it, usually a panel on the top or the bottom and/or top of the screen with a menu and a lot of other practical services you may never even notice.
The most important part of any desktop is the window manager, this is the application that handles window placements and movements. The window manager is what draws a border (or no border) around your windows and makes them maximize, minimize, moves and behave according to your preferences.
The GNU Network Object Model Environment
The GNU Network Object Model Environment, or GNOME, is the brain-child of Miguel de Icaza. GNOME was started in 1997 and has matured to provide a complete set of software libraries and clients.GNOME depends on a cognizant window managers to provide the desktop. GNOME user-friendly suite of clients provide a consistent and user-friendly desktop.
The K Desktop Environment
The K Desktop Environment (KDE) has been available for Linux and XFree86 since 1996. KDE was started by a German Linux software developer named matthias Ettrich, and has gone through several major revisions. KDE is a graphical desktop environment that includes a huge suite of clients, including a free office suite named KOffice.
KDE vs Gnome, What is the better desktop environment?
KDE and Gnome are complete desktop environments that consist of a large number of tightly integrated yet still separate pieces of software. Gnome uses a window manager called metacity, KDE uses kwin. Both these desktops can be used with any other window manager if you do not like the default choice.
Linux is like Lego. You can build your own desktop environment. Both KDE and Gnome are just big packages with software aimed to look and feel the same way, work well together and generally give you a nice experience. If you dislike a component, then replace it with something else. It's that simple.
Application that are "made for gnome" or "made for kde" can be used with any desktop. This only means that that the program use a set of library functions found in their underlying gnome-libs or kdelibs. You do not need to use the actual desktops to use the applications, software made for KDE and Gnome can be used with any window manager / desktop as long as you.