The white background represents the purity of the people. The red and blue circle in the middle form the Yin Yang that represent Heaven and Earth in perfect harmony. They compliment each other by being perfect opposites, such as, light and dark, day and night.
There are also four trigrams on each side of the yin yang also represent the balance and growth of the yin yang. The trigrams have many different interpretations in South Korea but are generally understood to represent the four elements (earth, fire, water, metal) and also to represent the family and heavens (mother/earth, father/heaven, and daughter and son)
Together all of the symbols and elements on the flag form to represent a perfect balance of harmony in the universe as well as the elements needed for a thriving country