In light of directives around the world to eliminate toxic materials in various technologies, finding lead-free materials with high piezoelectric responses is an important current scientific quest.As such, the recent discovery of a large electromechanical conversion near room temperature in (1-x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 compounds has attracted a lot of attention. Strikingly, the origin of such a strongly desired response is not conclusively understood, with various explanatory mechanisms having been proposed. Here, we report the development of a large-scale atomistic scheme providing a microscopic insight into this technologically-promising material. The use of such a scheme reveals that high piezoelectricity in (1-x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 originates from the existence of large fluctuations of the polarization in the orthorhombic state arising from the combination of flat free-energy surfaces, a fragmented local structure reflected in the relative small strength of the so-called percolating cluster, and the narrow temperature window around room temperature at which this orthorhombic phase is the equilibrium state. In addition to deepening the current knowledge on piezoelectricity, these findings have the potential to guide the design of other novel lead-free materials with large electromechanical responses.