For the first time, the origin of large electrostrain in pseudocubic BiFeO_{3}-based ceramics is verified with direct structural evidence backed by appropriate simulations. We employ advanced structural and microstructural characterizations of BiFeO_{3}-based ceramics that exhibit large electrostrain (>0.4%) to reveal the existence of multiple, nanoscale local symmetries, dominantly tetragonal or orthorhombic, which have a common, averaged direction of polarization over larger, meso- or microscale regions. Phase-field simulations confirm the existence of local nanoscale symmetries, thereby providing a new vision for designing high-performance lead-free ceramics for high-strain actuators.