We characterize the superionic phase transition and the lattice and electronic structures of the archetypal type-I superionic conductor alpha-AgI using extensive first-principles molecular dynamics calculations. We find that superionicity is signaled by a phase transition of the silver ions alone. In the superionic phase, the first silver shell surrounding an iodine displays a distinct dynamical structure that would escape a time-averaged characterization, and we capture this structure in a set of ordering rules. The electronic structure demonstrates a unique chemical signature of the weakest-bound silver in the first shell, which in turn is most likely to diffuse. Silver diffusion decreases upon melting, pointing to an unusual entropic contribution to the stability of the superionic phase.