In the Iranian culture, green symbolizes growth, happiness, unity, nature, vitality and the Iranian languages. Historically, a green and white flag in a triangular form used to be the flag of the Persians (Pars).
The traditional color of white symbolizes freedom, because white represents blankness and it is free to carry anything on it.
Red stands for martyrdom. In the Iranian culture, it symbolizes bravery, fire, life, love, warmth, and sophistication. Historically, a red and white flag in a triangular form used to be the flag of the Medes (Mada).
A lengthy discussion of the historical flags of Iran and of empires in the geographical area can be found here.