A frequency at which the system's kinetic energy exactly equals its potential energy. For a mechanical system, this corresponds to a frequency at which the system's inertial force is exactly balanced by the restoring spring force. For an electrical system, this corresponds to a frequency at which the system's inductive impedance is exactly balanced by its capacitive impedance.
Most mechanical systems have many natural frequencies. If a mechanical system (such as a resonator) is deformed and the released, it will vibrate with some combination of its natural frequencies.
Also see resonance.