I only found out today about the meaning of the flag after being a korean language student for half a year. Shame on me!
The flag, called "Tae Kuk," symbolizes the thought, philosophy, and mysticism of the Far East.
The circle in the center, red upper half and blue lower half, represents absolute, or the essential unity of all being. The Yang (positive) and the Yin (negative) divisions within the circle represent duality. Examples of duality are heaven and hell, fire and water, life and death, good and evil, or night and day
The four trigrams also indicate the duality of opposites and balances. In the upper left trigram, three unbroken lines symbolize Heaven; opposite them in the lower right, three broken lines represent Earth.
In the upper right trigram, two broken lines separated by an unbroken line is the symbol of Water; opposite them is Fire, symbolized by two unbroken lines separated by a broken line. Symbolic of the nation is the white background (the land), the circle (people), and the four trigrams (the government). All three make up the essential elements of the nation.