The Next Generation Virgo Cluster Survey (NGVS) is a program that uses the 1 deg(2) MegaCam instrument on the Canada-France-Hawaii Telescope to carry out a comprehensive optical imaging survey of the Virgo cluster, from its core to its virial radius-covering a total area of 104 deg(2)-in the u*griz bandpasses. Thanks to a dedicated data acquisition strategy and processing pipeline, the NGVS reaches a point-source depth of g approximate to 25.9mag (10 sigma) and a surface brightness limit of mu(g) similar to 29 mag arcsec(-2) (2 sigma above the mean sky level), thus superseding all previous optical studies of this benchmark galaxy cluster. In this paper, we give an overview of the technical aspects of the survey, such as areal coverage, field placement, choice of filters, limiting magnitudes, observing strategies, data processing and calibration pipelines, survey timeline, and data products. We also describe the primary scientific topics of the NGVS, which include: the galaxy luminosity and mass functions; the color-magnitude relation; galaxy scaling relations; compact stellar systems; galactic nuclei; the extragalactic distance scale; the large-scale environment of the cluster and its relationship to the Local Supercluster; diffuse light and the intracluster medium; galaxy interactions and evolutionary processes; and extragalactic star clusters. In addition, we describe a number of ancillary programs dealing with "foreground" and "background" science topics, including the study of high-inclination trans-Neptunian objects; the structure of the Galactic halo in the direction of the Virgo Overdensity and Sagittarius Stream; the measurement of cosmic shear, galaxy-galaxy, and cluster lensing; and the identification of distant galaxy clusters, and strong-lensing events.