We present the main results from our 940 ks observation of the Chandra Deep Field-South using the source catalog described in an accompanying paper by Giacconi et al. We extend the measurement of source number counts to 5.5 × 10-17 ergs cm-2 s-1 in the soft 0.5-2 keV band and 4.5 × 10-16 ergs cm-2 s-1 in the hard 2-10 keV band. The hard-band log N-log S shows a significant flattening (slope 0.6) below ≈10-14 ergs cm-2 s-1, leaving at most 10%-15% of the X-ray background to be resolved, the main uncertainty lying in the measurement of the total flux of the X-ray background (XRB). On the other hand, the analysis in the very hard 5-10 keV band reveals a relatively steep log N-log S (slope 1.3) down to 10-15 ergs cm-2 s-1. Together with the evidence of a progressive flattening of the average X-ray spectrum near the flux limit, this indicates that there is still a nonnegligible population of faint hard sources to be discovered at energies not well probed by Chandra, which possibly contributes to the 30 keV bump in the spectrum of the XRB. We use optical redshifts and identifications, obtained with the Very Large Telescope, for one-quarter of the sample to characterize the combined optical and X-ray properties of the Chandra Deep Field-South sample. Different source types are well separated in a parameter space that includes X-ray luminosity, hardness ratio, and R-K color. Type II objects, while redder on average than the field population, have colors that are consistent with being hosted by a range of galaxy types. Type II active galactic nuclei are mostly found at z 1, in contrast with predictions based on active galactic nucleus population synthesis models, thus suggesting a revision of their evolutionary parameters.