Buddhism is believed to have entered China when it came along with traders along the silk roads. It reached China as early as the second century BCE. The main way that Buddhist thought influenced China was by causing Buddhism to become a very popular religion.
Bentley and Ziegler argue (on p. 235 in the brief second edition of Traditions & Encounters) that Buddhism was popular in China because it was an intellectually sophisticated religion, because it set high standards of morality, and because it promised people salvation in a way that Confucianism really did not emphasize. For these reasons, many Chinese became Buddhist.
Their embrace of Buddhism led that faith to become a very important part of Chinese life. Monasteries appeared in all the major cities of China. Monasteries (like those in Western Europe in the Middle Ages) accumulated large estates that were donated to them. This meant that the monasteries were wealthy and important parts of the Chinese economy. They often helped peasants get by in hard economic times. Finally, Bentley and Ziegler say that Buddhism affected China by causing many Chinese to go on pilgrimages to India. This deepened the importance of the faith in China.
Thus, Buddhist thought affected China by leading to the conversion of many people. This, in turn, made Buddhism and Buddhist religious organizations a central part of Chinese society.