Could somebody point me to resources that would explain what full screen actually is?
What's the point of it? It seems to be more than just a window that has the client are taking the whole screen.
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In the old days a fullscreen mode was sometimes also called an "exclusive mode". The clue here is in the name - such a mode has exclusive control of the screen and other video hardware; nothing else can use it. Because it doesn't need to share resources with other programs, and doesn't need to co-operate nicely with other programs, it can be somewhat more agressive in it's use of the hardware, which can result in higher performance. A windowed mode by comparison does have to play nice with other programs you may be running, so it doesn't get to take what may be more optimal paths in the driver.
How this manifests to your program depends on your API of choice. Under D3D you must explicitly select a fullscreen mode whereas OpenGL has no such concept (but presumably the driver is able to make some intelligent decisions during context creation time).
Some further info here from an SO question a while back: https://stackoverflow.com/questions/304669/why-direct3d-application-performs-better-in-full-screen-mode (with a slightly heavier focus on behaviour of the DWM in Windows Vista/7 than is necessary for this current question, but it's all relevant nonetheless).
There are several benefits of fullscreen:
Fullscreen can also be used by non-game applications, typically embedded "kiosk" or information systems which have a single application "take over" the whole screen.
Note that using fullscreen mode for security (i.e. prevent access to desktop or other apps) is not a good idea and has historically been a security hole in many kiosk-type systems.