Turbo codes are known as a class of error-correcting codes which have high error-correcting performance with efficient decoding algorithm. Characteristics of the iterative decoding algorithm have been studied in detail through a variety of numerical experiments, but theoretical results are still insufficient. In this paper, this issue is addressed from the information geometrical viewpoint. As a result, a mathematical framework for analyzing turbo codes is obtained, and some of the fundamental properties of turbo decoding are elucidated based on this framework. Recently, it has been pointed out that the turbo decoding algorithm is related to the decoding algorithm of low-density parity check codes, the computation method of Bethe approximation in statistical physics, and the belief propagation algorithm of Bayesian networks. The mathematical framework given in the present paper can also be used to analyze these wide classes of iterative computation methods, and hence represent a new analysis tool.