Hangul Day
Before the creation of Hangul, people in Korea (known as Joseon at the time) primarily wrote using Classical Chinese alongside native phonetic writing systems that predate Hangul by hundreds of years, including idu, hyangchal, gugyeol, and gakpil. However, due to the fundamental differences between the Korean and Chinese languages, and the large number of characters needed to be learned, there was much difficulty in learning how to write using Chinese characters for the lower classes, who often didn't have the privilege of education. To assuage this problem, King Sejong created the unique alphabet known as Hangul to promote literacy among the common people.
Chinese family of scripts
The Hangul alphabet introduced in the 15th century was much simpler, and specifically designed for the sounds of Korean.
The alphabet makes systematic use of modifiers corresponding to features of Korean sounds.
Although Hangul is unrelated to Chinese characters, its letters are written in syllabic blocks that can be interspersed with Hanja. 
Such a Korean mixed script became the usual way of writing the language, with roots of Chinese origin denoted by Hanja and all other elements rendered in Hangul. Hanja is still used (but not very commonly like the Japanese) and is required in both North and South Korea.