From AMS Glossary
A region of sharply reduced precipitation on the lee side of an orographic barrier, as compared with regions upwind of the barrier.
Slopes facing windward with respect to prevailing or seasonal moisture-bearing flows typically experience heavy orographic precipitation. To the lee of the barrier, however, the sinking air warms, dries, and becomes more stable, suppressing precipitation. Two dramatic and often-cited examples are the Ghat Mountains of western India, which receive annually more than 600 cm of rainfall at locations on their western slopes but 60 cm or less on their eastern slopes, and the island of Hawaii, where up to 450 cm of rain falls on the slopes facing the northeast trade winds, but less than 100 cm falls at locations on the lee side of the island. A good example of rain shadow in the United States is the region east of the Sierra Nevadas; there the prevailing westerly winds deposit most of their moisture on the western slopes of the range, whereas to the east lies the Great Basin desert.