Using the Long Wavelength Spectrometer (LWS) onboard the Infrared Space Observatory (ISO), we have observed thermal water vapor emission from a roughly circular field of view approximately 75 arc seconds in diameter centered on the Orion BN-KL region. The Fabry-Perot line strengths, line widths, and spectral line shifts observed in eight transitions between 71 and 125 microns show good agreement with models of thermal emission arising from a molecular cloud subjected to a magnetohydrodynamic C-type shock. Both the breadth and the relative strengths of the observed lines argue for emission from a shock rather than from warm quiescent gas in the Orion core. Though one of the eight transitions appears anomalously strong, and may be subject to the effects of radiative pumping, the other seven indicate an H2O/H2 abundance ratio of order 5E-4, and a corresponding gas-phase oxygen-to-hydrogen abundance ratio of order 4E-4. Given current estimates of the interstellar, gas-phase, oxygen and carbon abundances in the solar vicinity, this value is consistent with theoretical shock models that predict the conversion into water of all the gas-phase oxygen that is not bound as CO. The overall cooling provided by rotational transitions of H2O in this region appears to be comparable to the cooling through rotational lines of CO, but is an order of magnitude lower than cooling through H2 emission. However, the model that best fits our observations shows cooling by H2O and CO dominant in that portion of the post-shock region where temperatures are below ~ 800 K and neither vibrational nor rotational radiative cooling by H2 is appreciable.