The Pierre Auger Observatory is designed to study cosmic rays with energies greater than 1019eV. Two sites are envisaged for the observatory, one in each hemisphere, for complete sky coverage. The southern site of the Auger Observatory, now approaching completion in Mendoza, Argentina, features an array of 1600 water-Cherenkov surface detector stations covering 3000km2, together with 24 fluorescence telescopes to record the air shower cascades produced by these particles. The two complementary detector techniques together with the large collecting area form a powerful instrument for these studies. Although construction is not yet complete, the Auger Observatory has been taking data stably since January 2004 and the first physics results are being published. In this paper we describe the design features and technical characteristics of the surface detector stations of the Pierre Auger Observatory.