The Wide Field Infrared Survey Telescope (WFIRST), which is entering Phase B for a launch in 2026, is NASA’s next large space observatory after the James Webb Space Telescope. In addition to the primary science carried out by The Wide Field Instrument (WFI), which is designed to carry out surveys of galaxies in the near infrared, explore the properties of dark energy and dark matter, and carry out a microlensing survey to complete the census of exoplanets, there will be a technology demonstration of a Coronagraph Instrument (CGI) for very high-contrast imaging and spectroscopy of nearby exoplanets. The CGI will incorporate two coronagraph types and demonstrate low- and high-order wavefront correction for the first time on a space telescope. Operating in the visible, it will consist of a direct imaging camera and a lenslet based integral field spectrograph, both using electron-multiplying CCDs in the focal plane, as well as polarizers allowing direct imaging in separate polarization states. Written by the lead science and engineering team, supported by two science investigation teams (SITs – https://wfirst.gsfc.nasa.gov/science/fswg/scienceteam.html), this paper presents an overview of the technology requirements on the instrument, the instrument design, and the operational plans to demonstrate exoplanet imaging and spectroscopic capability. Also described is how CGI will advance algorithms for extracting planet images from the background and retrieving spectra from a space IFS. Once the core performance is successfully demonstrated, CGI will also be used in the latter part of the mission for a dedicated science and Guest Observer (GO) program. This paper thus also describes the potentially revolutionary science that will be enabled through direct imaging and spectroscopy of known radial velocity planets and debris disks as seen in reflected light.