According to BusinessDictionary.com, an organic organization is an: organizational structure characterized by (1) Flatness: communications and interactions are horizontal, (2) Low specialization: knowledge resides wherever it is most useful, and (3) Decentralization: a great deal of formal and informal participation in decision making. 

I like to think an organic organization is a purpose-driven journey of growth through engagement, transparency, retrospection, communication, and improvement.