Explain the difference between vegetation growth on the upwind side and the rain shadow side of a mountain

Wind and moist air is drawn by the prevailing winds towards the top of the mountains, where it condenses and precipitates before it crosses the top. The air, without much moisture left, advances across the mountains creating a drier side called the "rain shadow".

The windward side of the mountain is the side of the mountain that the wind blows into. This side is where all the rain tends to be because of the air cools as it rises, making clouds. The opposite side is called the leeward side. This is where the air sinks, leaving the side much more warm and dry.