The Near-Inrared Spectrograph (NIRSpec) on the James Webb Space Telescope (JWST) is a very versatile instrument, offering multiobject and integral field spectroscopy with varying spectral resolution ($\sim$30 to $\sim$3000) over a wide wavelength range from 0.6 to 5.3 micron, enabling scientists to study many science themes ranging from the first galaxies to bodies in our own Solar System. In addition to its integral field unit and support for multiobject spectroscopy, NIRSpec features several fixed slits and a wide aperture specifically designed to enable high precision time-series and transit as well as eclipse observations of exoplanets. In this paper we present its capabilities regarding time-series observations, in general, and transit and eclipse spectroscopy of exoplanets in particular. Due to JWST's large collecting area and NIRSpec's excellent throughput, spectral coverage, and detector performance, this mode will allow scientists to characterize the atmosphere of exoplanets with unprecedented sensitivity.