We present details of the construction and characterization of the coaddition of the Sloan Digital Sky Survey (SDSS) Stripe 82 ugriz imaging data. This survey consists of 275 deg2 of repeated scanning by the SDSS camera over -50° ≤ α ≤ 60°and -1.°25 ≤ δ ≤ +1.°25 centered on the Celestial Equator. Each piece of sky has 20 runs contributing and thus reaches 2 mag fainter than the SDSS single pass data, i.e., to r 23.5 for galaxies. We discuss the image processing of the coaddition, the modeling of the point-spread function (PSF), the calibration, and the production of standard SDSS catalogs. The data have an r-band median seeing of 1.″1 and are calibrated to ≤1%. Star color-color, number counts, and PSF size versus modeled size plots show that the modeling of the PSF is good enough for precision five-band photometry. Structure in the PSF model versus magnitude plot indicates minor PSF modeling errors, leading to misclassification of stars as galaxies, as verified using VVDS spectroscopy. There are a variety of uses for this wide-angle deep imaging data, including galactic structure, photometric redshift computation, cluster finding and cross wavelength measurements, weak lensing cluster mass calibrations, and cosmic shear measurements.