OK. Step by step! But you really should do a bit of reading too.

X is the server program that creates your graphical interface. Properly it's called the xorg server but people often say X. It paints all the pretty pictures on the screen, collects keystrokes and mouse clicks and passes them on to its clients, the graphical applications. The clients then react to these and tell X whenever it needs to repaint their windows.

In most distros, X is brought up automatically by a program called a display manager, which then provides you with a login box. If you kill X with ctrl-alt-backspace, the display manager simply starts it again and you're back to your login screen. But you can also have a more basic Linux system without a display manager. Then you get a text console to log in at and you start X by hand using the startx command. I prefer to work like that because it makes for a less complex system.

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Hazel,
Thanks for taking the time to post. I know you said I need to do a bit of reading.
Your description keeps it reasonably straightforward, even though I struggle to follow most of it.