If the fibers in wood are kind of like your fingers, working cross grain refers to working at right angles to the fingers/fibers—that is, across the knuckles. Many tools for working cross grain are designed with a vertical knife to preslice across the grain, followed by a diagonally set blade to sweep out the wood behind. The combination of knife and diagonal blade (skewed iron) leaves a clean shoulder and a smooth surface. Wood will respond to moisture in the environment and will expand and contract across the grain in wetter and drier weather.
Using the same analogy as just above, working end grain is the equivalent of your running one hand over the fingertips of your other hand. Each finger supports the other until you get to your pinky, which tends to get pushed away from the rest of the pack. This is the central challenge of end grain working (aside from maintaining sharpness)— keeping the last little fibers supported so that they do not break off before they are cut.
Like pulling down the length of the fingers on your hand, working long grain does not tend to separate the fibers of the wood or catch on the ends. But just as there is roughness around your knuckles, the wood has knots that disturb the even now of the grain. The length of wood is usually defined by long grain: a piece will not get longer and shorter with changes in humidity, but it will get fatter and skinnier.