IrisCode is an iris recognition algorithm developed in 1993 and continuously improved by Daugman. Understanding IrisCode's properties is extremely important because over 60 million people have been mathematically enrolled by the algorithm. In this paper, IrisCode is proved to be a compression algorithm, which is to say its templates are compressed iris images. In our experiments, the compression ratio of these images is 1:655. An algorithm is designed to perform this decompression by exploiting a graph composed of the bit pairs in IrisCode, prior knowledge from iris image databases, and the theoretical results. To remove artifacts, two postprocessing techniques that carry out optimization in the Fourier domain are developed. Decompressed iris images obtained from two public iris image databases are evaluated by visual comparison, two objective image quality assessment metrics, and eight iris recognition methods. The experimental results show that the decompressed iris images retain iris texture that their quality is roughly equivalent to a JPEG quality factor of 10 and that the iris recognition methods can match the original images with the decompressed images. This paper also discusses the impacts of these theoretical and experimental findings on privacy and security.