To expand on the rain shadow effect - air going up over a mountain range cools and water condenses out of the air, falling as precipitation. Then as it comes down over the opposite side, it warms back up and is at much lower humidity (since it lost water as precipitation, and since warm air can hold more water). So you're going to get much less condensing water/clouds/precipitation on the back side of the mountain range. If you have a prevailing wind such that this is mostly happening in the same direction, you'll have a rain shadow desert.

You can even get rain shadow deserts over the ocean, on the lee side of a mountainous island.