Umbrella sampling Monte Carlo simulations are used to calculate free energy barriers to homogeneous liquid-vapor nucleation in the superheated Lennard-Jones fluid. The calculated free energy barriers decrease with increased superheating and vanish at the spinodal curve. A statistical geometric analysis reveals the existence of two types of voids: Small interstitial cavities, which are present even in the equilibrium liquid, and much larger cavities that develop as the system climbs the nucleation free energy barrier. The geometric analysis also shows that the average cavity size within the superheated liquid is a function of density but not of temperature. The critical nucleus for the liquid-vapor transition is found to be a large system-spanning cavity that grows as the free energy barrier is traversed. The weblike cavity is nonspherical at all superheatings studied here, suggesting a phenomenological picture quite different from that of classical nucleation theory.