I believe the term refers to architectural styles which draw inspiration and influence from forms seen in nature. Or, architecture that is built to blend seamlessly into natural settings like cliffsides or forested areas.
Organic architecture is part of an artistic movement which promotes harmony between the places inhabited by humans and the natural surroundings. It promotes design that aims to be sympathetic and well-integrated with its natural context, distributing in the best possible way the space to allow the unification of environmental elements with architectural elements (usually made with natural materials).