The Wide Field Imager (WFI) is one of two instruments for the Advanced Telescope for High-ENergy Astrophysics (Athena). In this paper we summarise three of the many key science objectives for the WFI – the formation and growth of supermassive black holes, non-gravitational heating in clusters of galaxies, and spin measurements of stellar mass black holes – and describe their translation into the science requirements and ultimately instrument requirements. The WFI will be designed to provide excellent point source sensitivity and grasp for performing wide area surveys, surface brightness sensitivity, survey power, and absolute temperature and density calibration for in-depth studies of the outskirts of nearby clusters of galaxies and very good high-count rate capability, throughput, and low pile-up, paired with very good spectral resolution, for detailed explorations of bright Galactic compact objects.