We present results from a large volume simulation of hydrogen reionization. We combine 3D radiative transfer calculations and an N-body simulation, describing structure formation in the intergalactic medium, to detail the growth of H II regions around high-redshift galaxies. Our simulation tracks 10243 dark matter particles, in a box of comoving side length 65.6 Mpc h-1. This large volume allows us to accurately characterize the size distribution of H II regions throughout most of the reionization process. At the same time, our simulation resolves many of the small galaxies likely responsible for reionization. It confirms a picture anticipated by analytic models: H II regions grow collectively around highly clustered sources and have a well-defined characteristic size, which evolves from a sub-Mpc scale at the beginning of reionization to R > 10 Mpc toward the end. We present a detailed statistical description of our results and compare them with a numerical scheme based on the analytic model by Furlanetto and coworkers. We find that the analytic calculation reproduces the size distribution of H II regions and the 21 cm power spectrum of the radiative transfer simulation remarkably well. The ionization field from the simulation, however, has more small-scale structure than the analytic calculation, owing to Poisson scatter in the simulated abundance of galaxies on small scales. We propose and validate a simple scheme to incorporate this scatter into our calculations. Our results suggest that analytic calculations are sufficiently accurate to aid in predicting and interpreting the results of future 21 cm surveys. In particular, our fast numerical scheme is useful for forecasting constraints from future 21 cm surveys and in constructing mock surveys to test data analysis procedures.