The Chinese character for "West" is 西, pronounced [xī].
In ancient time, 西 was written like the following:
This pictograph shows a bird resting on its nest. The bird returns to its nest at sunset time, and the sun sets in the west. So the pictograph acquired the meaning of "West." The character as it exists today is simpler than its ancient form, but you can still tell the connection between the two.
Since China is located on the eastern end of the Eurasian continent, the Chinese traditionally viewed their country the "Eastern Land." As result, historically, 西 denoted "western" and also “foreign." For example, Central Asia was called Xī Yù, "Western Territory." Tomato, which was not native to China, came to be known as Xī Hóng Shì, "Western Red Persimmon."
Buddhism came to China from India, by way of Central Asia. One of China's classical novels is Xī Yóu jì, "West Journey Tale," commonly translated into English as Journey to the West, which tells the fantastic story how a Chinese monk, accompanied by three rehabilitated monsters, travels to India to bring Buddhist sutra to China.
In the Pure Land school of Buddhism, there is a "a paradise of ultimate bliss," to which good people eventually ascend. It is believed that this paradise is located in the west. In Chinese, this is known as Xī Tiān, "Western Heaven" or "Western Paradise."