Within the Born–Oppenheimer (adiabatic) approximation, this is associated with an energy minimum on a potential energy surface. Structural stability implies that any change in the coordinates of the nuclei can only increase the total energy.
Source:
PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1964 (https://doi.org/10.1351/pac199971101919)