@sm52 For example, a recording of the background noise of a device or environment can be analyzed to show problem frequencies and their amplitudes, and/or the overall noise level. So, when changes are made to improve things, the same analysis can be used to quantify the improvement, and guide further ones. I particularly like it for self/background noise, since that's not a signal that you can inject into the system in the normal sense.
But, it can useful for analyzing signals as well -- the frequency response of a section of music, for example. So, that trumpet harmonic or bass guitar or whatever that doesn't sound right -- you can easily identify the exact frequency and level and therefore make compensations as necessary.