The photometric and morphological properties, as well as the star formation history, of the Draco dwarf spheroidal galaxy are analyzed on the basis of wide-field CCD photometry of the resolved stars covering about 1 deg2. Draco is at a distance of d=80+/-7 kpc and has a metallicity, [Fe/H], of -1.8+/-0.2. No metallicity gradient is detected. The star surface density distribution can be fitted by a single exponential law of scale length α=5.0′+/-0.1′. The central surface magnitude is μ''V''=24.4+/-0.5, and the core radius is rc=7.5′+/-0.3′ (equivalent to rc=175+/-7 pc). Within errors, the same scale lengths are found for the density profiles along the semimajor and semiminor axes (rescaled to semimajor-axis units, using the ellipticity of the galaxy) of Draco. There are hence no evidences of a tidal tail associated with Draco. The tidal radius of the galaxy is found to be rt~=42' (~=1 kpc). The possibility that the large mass-to-light relation in Draco could be accounted for by a convenient spatial orientation is tested. An upper limit to Draco's size along the line of sight is ~14 kpc. This is too small to account for the velocity dispersion of Draco if it were due to projection effects only, and it implies that other mechanisms (e.g., dark matter) are required. The stellar population of Draco is mainly old. Although some intermediate-age population is present in Draco, most of the star formation (up to 90%) took place before ~10 Gyr ago. No significant star formation activity is detected in the last ~2 Gyr. Two methods (partial model and subgiant) have been used to investigate the star formation history of Draco, both producing results in good qualitative agreement. No difference is found between the scale lengths of the distributions of old (>~9 Gyr) and young (~2-3 Gyr) stars, indicating either that both populations were formed under the same kinematic conditions, or that any initial difference was afterward erased.