The search for energy-efficient and environmentally friendly cooling technologies is a key driver for the development of magnetic refrigeration based on the magnetocaloric effect (MCE). This phenomenon arises from the interplay between magnetic and lattice degrees of freedom that is strong in certain materials, leading to a change in temperature upon application or removal of a magnetic field. Here we explore in detail an emerging material, Mn1-xFexNiSi0.95Al0.05, with an exceptionally large isothermal entropy at room temperature. By combining experimental and theoretical methods we outline the microscopic mechanism behind the large MCE in this material. It is demonstrated that the competition between the Ni2In-type hexagonal phase and the TiNiSi-type orthorhombic phase, that coexist in this system, combined with the distinctly different magnetic properties of these phases, is a key parameter for the functionality of this material for magnetic cooling.