Natural frequency is the rate at which a system oscillates in a single direction of freedom without outside interference. An example of this is the motion of a suspended spring with a weight attached to its bottom. When released, the spring oscillates to its own natural frequency.
The exact rate of a mechanical system's natural frequency is determined by a number of variable factors. First, the stiffness of the spring provides resistance to the oscillations and tends to arrest the motion. Second, the mass of the weight tends to add more energy and speed up the frequency. Finally, the radian frequency is obtained by dividing the stiffness by the mass.