The high-frequency peaked BL Lac PKS 2155-304 at redshift z=0.117 has been detected with high significance (similar to45sigma) at energies greater than 160 GeV, using the H.E.S.S. stereoscopic array of imaging air-Cherenkov telescopes in Namibia. A strong signal is found in each of the data sets corresponding to the dark periods of July and October, 2002, and June-September, 2003. The observed flux of VHE gamma rays shows variability on time scales of months, days, and hours. The monthly-averaged integral flux above 300 GeV varies between 10% and 60% of the flux observed from the Crab Nebula. Energy spectra are measured for these individual periods of data taking and are characterized by a steep power law with a time-averaged photon index of Gamma=3.32+/-0.06. An improved chi(2) per degree of freedom is found when either a power law with an exponential cutoff energy or a broken power law are fit to the time-averaged energy spectrum. However, the significance of the improvement is marginal (similar to2sigma). The suggested presence of features in the energy spectrum may be intrinsic to the emission from the blazar, or an indication of absorption of TeV gamma rays by the extragalactic infrared background light.