This is an example of how a typical GNOME session goes, under a modern desktop environment in a Linux system. It's very similar to how things work under other environments, assuming they work on top of X.
When a Linux system starts X, the X server comes up and initializes the graphic device, waiting for requests from clients. First a program called gnome-session starts, and sets up the working session. A session includes things such as applications I always open, their on-screen positions, and such. Next, the panel gets started. The panel appears at the bottom (usually) and it's sort of a dashboard for the windowing environment. It will let us launch programs, see which ones are running, and otherwise control the working environment. Next, the window manager comes up. Since we're using GNOME, it could be any of several different window managers, but in this case we'll assume we're running Sawfish. Finally, the file manager comes up (gmc or Nautilus). The file manager handles presentation of the desktop icons (the ones that appear directly on the desktop). At this point my GNOME environment is ready to work.
So far all of the programs that have been started are clients, connecting to the X server. In this case the X server happens to be in the same computer, but as we saw before, it need not be.
We'll now open an xterm to type some commands. When we click on the xterm icon, the panel spawns, or launches, the xterm application. It's another X client application, so it starts, connects to the X server and begins displaying its stuff. When the X server assigns screen space for my xterm, it lets the window manager (Sawfish) decorate the window with a nice titlebar, and decide where it will be on screen.
Let's do some browsing. We click on the Netscape icon on the panel, and up comes a browser. Keep in mind that this browser doesn't use GNOME's facilities, nor does it use the Gtk toolkit. It looks a bit out of place here... also, it doesn't interact very nicely with the rest of the environment. I'll open the "File" menu. Motif is providing the on-screen controls, so it's the Motif library's job to make the appropriate calls to the underlying Xlib, draw the necessary on-screen elements to display the menu and let me select the "exit" option, closing the application.
Now I open a Gnumeric spreadsheet and start doing some stuff. At some point I need to do some work on the xterm I had open, so I click on it. Sawfish sees that, and, being in charge of managing windows, brings the xterm to the top and gives it focus so I can work there.
After that, I go back to my spreadsheet, now that I'm finished I want to print my document. Gnumeric is a GNOME application, so it can use the facilities provided by the GNOME environment. When I print, Gnumeric calls the gnome-print library, which actually communicates with the printer and produces the hard copy I need.