The Cosmic Origins Spectrograph (COS) is a moderate-resolution spectrograph with unprecedented sensitivity that was installed into the Hubble Space Telescope (HST) in 2009 May, during HST Servicing Mission 4 (STS-125). We present the design philosophy and summarize the key characteristics of the instrument that will be of interest to potential observers. For faint targets, with flux F λ ≈ 1.0 × 10-14 erg cm-2 s-1 Å-1, COS can achieve comparable signal to noise (when compared to Space Telescope Imaging Spectrograph echelle modes) in 1%-2% of the observing time. This has led to a significant increase in the total data volume and data quality available to the community. For example, in the first 20 months of science operation (2009 September-2011 June) the cumulative redshift pathlength of extragalactic sight lines sampled by COS is nine times than sampled at moderate resolution in 19 previous years of Hubble observations. COS programs have observed 214 distinct lines of sight suitable for study of the intergalactic medium as of 2011 June. COS has measured, for the first time with high reliability, broad Lyα absorbers and Ne VIII in the intergalactic medium, and observed the He II reionization epoch along multiple sightlines. COS has detected the first CO emission and absorption in the UV spectra of low-mass circumstellar disks at the epoch of giant planet formation, and detected multiple ionization states of metals in extra-solar planetary atmospheres. In the coming years, COS will continue its census of intergalactic gas, probe galactic and cosmic structure, and explore physics in our solar system and Galaxy.