Before Wilson's RG approach, there was an astonishing empirical fact to explain: The coincidence of the critical exponents (i.e., the exponents of the reduced-temperature dependence of several quantities near a second order phase transition) in very disparate phenomena, such as magnetic systems, superfluid transition (Lambda transition), alloy physics, etc. So in general, thermodynamic features of a system near a phase transition depend only on a small number of variables, such as the dimensionality and symmetry, but are insensitive to details of the underlying microscopic properties of the system.