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There are quite a number of frequency responses depending on what you take as the excitation and the response. You normally plot the frequency response of a transfer function (which equals the ratio of response/excitation).
One important use of the frequency response is to figure out if a closed-loop system is stable or not. For this we use the loop gain frequency response. From the loop gain transfer function, we look at things like the phase margin and gain margin which will tell us if the closed loop system is stable or not. And if the system is stable, it will tell us how far away we are from being unstable.
If you search the EDAboard for "Bode" "phase margin" and "gain margin", you will find a number of discussions on these topics.
EVERY SUBSTANCE ON THIS EARTH WILL HAVE A DIFFERENT RESPONSE FOR DIFFERENT FREQUENCIES. THE PERFORMANCE AND GENERAL HEALTHINESS OF THE CIRCUIT/OBJECT/BODY CAN BE JUDGED BY DRAWING A FREQUENCE RESPONSE CURVE/DIAGARM. STABLE AND LINEAR RESPONSE WILL BE CONFINED TO CERTAIN BAND OF FREQUENCIES WHICH WE GENERALLY TERM IT AS BANDWIDTH.
Such as v_c'post, from the frequency response curve we can analysis whether the closed loop system is stable or not under the condition of circuit spec. The PM and GM is the most keypoint which should be obtained in the frequency response curve.
The frequency response is very usefull and required in some situations for example if u designing a filter circuit u need the frequency response to determine the bandwidth limits of that filter by plotting the output of the filter in db against the frequency