The origin of sonoluminescence, the conversion of acoustic energy into ultraviolet/visible radiation in liquids, has remained elusive. We propose that the emission arises from electrons confined to voids in the hot, dense fluid formed during the final stages of bubble collapse. Such electrons are produced by high-temperature ionization of the bubble constituents. A hard-sphere-based model was developed for the fluid structure, thermodynamics, and confined electron emission. The model is consistent with the observed spectral distributions, power output, and time scale associated with emission from single cavitating rare gas bubbles. Effective temperatures during emission in the 200-700 nm spectral window are predicted to range from 20 000 to 60 000 K.