Why does styling the background of the body element affect the entire screen?

Quote from http://www.w3.org/TR/CSS21/colors.html

The background of the root element becomes the background of the canvas and covers the entire canvas, anchored (for 'background-position') at the same point as it would be if it was painted only for the root element itself. The root element does not paint this background again.

The body element is the root-element, and thus, as required by the CSS rules it loses its background style and the background style is applied to the containing canvas (the webpage area in the browser), therefor the entire screen is blue. The other properties stay with the element (e.g. the border).

From CSS: The Definitive Guide by Eric Meyer

In CSS values are never propagated upward; that is, an element never passes values up to its ancestors. There is an exception to the upward propagation rule in HTML: background styles applied to the body element can be passed to the html element, which is the document's root element and therefore defines its canvas.

So when you add the background-color: blue; declaration to the body element, this value is propagated to the html element (which is also the root element). Add this declartion to see it for yourself.

html {
    background-color: grey;
}