A rain shadow is dry, because as moist air masses rise to top a mountain range, they cool, some of their water vapor condenses as rain, and they lose water. Thus on the windward side (or leeward side) it is dry, often arid desert.
Good examples (in the United States, at least; rain shadows occur worldwide) are in the deserts of the Basin and Range Province, or the dry areas east of the Cascade Mountains of Oregon and Washington State. The apty-named Death Valley is another good American example; it is behind both the Coastal Range of California and the Sierra Nevada range, and is one of the driest places on Planet Earth.