A desktop environment is a graphical user interface (GUI) built on the metaphor of a desktop. The desktop lets a user manipulate files and programs graphically and do most system tasks without having to type in commands. Desktop environments replaced the command line interfaces of early computers and the vast majority of people now use a desktop environment for computing (though a few very experienced users actually prefer command line interfaces). In Linux, the desktop is not bound to the core kernel but runs on top of it, alongside whatever other programs the user has installed. This separation of the desktop environment from the kernel facilitates choice. It allows Linux distribution makers (and users) to not only choose from several different desktops, but also to run just a window manager (explained below) instead or indeed stick entirely to the command line environment.
Although Linux has several desktop environments to choose from, two are dominant in the competition for market share, KDE and Gnome. Happily it is possible to install any desktop environment on any mainstream Linux distribution. So although the very popular Ubuntu distribution usually ships with Gnome, it will just as easily work with KDE or one of the other desktop environments. It is even possible to have two desktop environments installed simultaneously and choose which to use whenever you log in (though you can't run both at once). So choice of desktop is down to an individuals preferences. Although any Linux desktop will meet your basic needs, each has a distinct philosophy and you are likely to find you prefer one over the others. Use the information which follows to guide your choice.
KDE
KDE is the older of the two market leaders and emphasises user choice and customisability. In many ways, KDE embodies what people expect from Linux: it is similar enough to Windows to make new users feel somewhat at home but caters for power users with its comprehensive configurability. It is often preferred by more experienced Linux users because of this. The flipside of the choice KDE offers is that there is more to learn. Very new users may feel more comfortable with Gnome which simplifies the desktop by limiting what users can do through the GUI. In 2008, KDE went through a major revamp designed to position it to take advantage of new technologies - including ones which will eventually update the desktop metaphor. Linus Torvalds (the creator of Linux) recommends KDE. KDE has many applications which have been specially written to take advantage of it, such as Amarok.
Gnome
The Gnome Desktop philosophy is to make things as easy as possible, even if that requires a one size fits all approach. Gnome developers typically research and decide upon a best practice for a particular desktop function then require the user to adjust (as eg Microsoft did with the new ribbon interface in Office 2007). The guidelines for Gnome call for all configuration options to be kept to a reasonable minimum to avoid user confusion. Despite this Gnome still offers plenty of choice concerning look and feel. Those who don't need to tailor a desktop to be just so and are happy to be guided down a particular path to accomplish tasks may prefer to use Gnome.
XFCE
XFCE is a lightweight Desktop Environment chiefly aimed at bringing a modern desktop to older hardware. It aims to be "fast and lightweight, whilst still being visually appealing and user friendly". XFCE demands fewer system resources so will run faster than Gnome or KDE and on a lower hardware spec than either require. It is designed to be more modular and therefore offer greater flexibility on what components are installed. Because of this it takes up less space on the disk and is quicker to install. However XFCE still looks visually attractive.
Etoile
toil is different from other desktops. The basic unit in Etoile is the object, with objects arranged into projects. Etoile's approach combines aspects of both folders and virtual desktops, with objects and tasks able to share data. Rather than run applications to manipulate files Etoile offers services which are micro programs which can be strung together to create a custom application shaped to what the user wants to do with the object. For example, Etoile does not assume a new document is a particular type such as text documentto be manipulated by a word processor. Rather it allows the user to drop in and combine whatever components are desired from text to tables to video. Though still in heavy development a stable version of Etoile has been released.
Window managers
A window manager is actually what most people have in mind when thinking about a desktop. The window manager is the part of a desktop environment which controls what is displayed on screen. It keeps track of which windows are open and provides a way to switch between them. The window manager ensures that application windows have a consistent look. Some window managers such as fluxbox can run independently of a desktop which means they can be squeezed into machines with less than 128 megs of ram.