However, we never mentioned how the X server handles manipulation of the clients' on-screen display areas (called windows). It's obvious, to anyone who's ever used a GUI, that you need to have control over the "client windows". Typically you can move and arrange them; change size, maximize or minimize windows. How, then, does the X server handle these tasks? The answer is: it doesn't.
One of X's fundamental tenets is "we provide mechanism, but not policy". So, while the X server provides a way (mechanism) for window manipulation, it doesn't actually say how this manipulation behaves (policy).
All that mechanism/policy weird stuff basically boils down to this: it's another program's responsibility to manage the on-screen space. This program decides where to place windows, gives mechanisms for users to control the windows' appearance, position and size, and usually provides "decorations" like window titles, frames and buttons, that give us control over the windows themselves. This program, which manages windows, is called (guess!) a "window manager".
"The window manager in X is just another client -- it is not part of the X window system, although it enjoys special privileges -- and so there is no single window manager; instead, there are many, which support different ways for the user to interact with windows and different styles of window layout, decoration, and keyboard and colormap focus."
The X architecture provides ways for a window manager to perform all those actions on the windows; but it doesn't actually provide a window manager.
There are, of course, a lot of window managers, because since the window manager is an external component, it's (relatively) easy to write one according to your preferences, how you want windows to look, how you want them to behave, where do you want them to be, and so on. Some window managers are simplistic and ugly (twm); some are flashy and include everything but the kitchen sink (enlightenment); and everything in between; fvwm, amiwm, icewm, windowmaker, afterstep, sawfish, kwm, and countless others. There's a window manager for every taste.
A window manager is a "meta-client", whose most basic mission is to manage other clients. Most window managers provide a few additional facilities (and some provide a lot of them). However one piece of functionality that seems to be present in most window managers is a way to launch applications. Some of them provide a command box where you can type standard commands (which can then be used to launch client applications). Others have a nice application launching menu of some sort. This is not standardized, however; again, as X dictates no policy on how a client application should be launched, this functionality is to be implemented in client programs. While, typically, a window manager takes on this task (and each one does it differently), it's conceivable to have client applications whose sole mission is to launch other client applications; think a program launching pad. And of course, people have written large amounts of "program launching" applications.