We provide an overview of the capabilities and performance of the Near-Infrared Spectrograph (NIRSpec) on the James Webb Space Telescope (JWST) when used in its multi-object spectroscopy (MOS) mode employing a novel Micro Shutter Array (MSA) slit device. The MSA consists of four separate 98 arcsec $\times$ 91 arcsec quadrants each containing $365\times 171$ individually addressable shutters whose open areas on the sky measure 0.20 arcsec $\times$ 0.46 arcsec on a 0.27 arcsec $\times$ 0.53 arcsec pitch. This is the first time that a configurable multi-object spectrograph has been available on a space mission. The levels of multiplexing achievable with NIRSpec MOS mode are quantified and we show that NIRSpec will be able to observe typically fifty to two hundred objects simultaneously with the pattern of close to a quarter of a million shutters provided by the MSA. This pattern is fixed and regular, and we identify the specific constraints that it yields for NIRSpec observation planning. We also present the data processing and calibration steps planned for the NIRSpec MOS data. The significant variation in size of the mostly diffraction-limited instrument point spread function over the large wavelength range of 0.6-5.3 $\mu$m covered by the instrument, combined with the fact that most targets observed with the MSA cannot be expected to be perfectly centred within their respective slits, makes the spectrophotometric and wavelength calibration of the obtained spectra particularly complex. These challenges notwithstanding, the sensitivity and multiplexing capabilities anticipated of NIRSpec in MOS mode are unprecedented, and should enable significant progress to be made in addressing a wide range of outstanding astrophysical problems.