The MIGHTEE large survey project will survey four of the most well-studied extragalactic deep fields, totalling 20 square degrees to μJy sensitivity at Giga-Hertz frequencies, as well as an ultra-deep image of a single ~1 deg2 MeerKAT pointing. The observations will provide radio con- tinuum, spectral line and polarisation information. As such, MIGHTEE, along with the excellent multi-wavelength data already available in these deep field, will allow a range of science to be achieved. Specifically, MIGHTEE is designed to significantly enhance our understanding of; the evolution of AGN and star-formation activity over cosmic time, as a function of stellar mass and environment, free of dust obscuration; the evolution of neutral hydrogen in the Universe and how this neutral gas eventually turns into stars after moving through the molecular phase, and how efficiently this can fuel AGN activity; the properties of cosmic magnetic fields and how they evolve in clusters, filaments and galaxies. MIGHTEE will reach similar depth to the aims of the SKA all-sky survey, and thus will provide a pilot to the cosmology experiments that will be carried by the SKA on much larger survey volume.