You can find as succinct a description of Zhu Xi's importance as any in the Taiwan middle-school textbook History of Chinese Culture, which notes that Zhu Xi spent a lifetime annotating the Confucian classics, and established his own academies to teach others.
朱熹對後世的影響力，台灣中學課本《中國文化史》也寫得很清楚：朱子畢生註解儒家典籍，並建立書院，教育子弟，對東亞思想界影響至為深遠。