If we take a look at the definition of frequency, we can see that this is an inverse value of time. Frequency tells us how many repetitions are done in a certain amount of time.
Here is an example of a sine signal pictured in two graphs: one is in time-domain, the other is in frequency domain. In both cases the vertical axis represents the amplitude, while the horizontal is time in one case and frequency in the other.
In time-domain we can see a shape of the signal in a certain amount of time (depends on how large the graph is horizontally), in frequency-domain we can see the position of the same signal on the frequency axis and it looks like a vertical line where the height of this line represents the amplitude. In this case we have depicted a single sine frequency and that is the most explicit case – it is simple to view in both graphs.
Should we have a union of two frequencies, like for example f and 2f, the graph would look like this:
In time-domain it is not so obvious anymore what's going on, while in the frequency-domain we can clearly see that we deal with a union of two sine signals. We can also see their frequency and amplitude very clearly.
In audio we operate with clean and periodical signals only in laboratory testing, while in music this type of signals are very rare. Music is a complex sum of various sine waves and observing this type of signal in time-domain is of limited use.
On the other hand, if we observe a complex signal in frequency-domain, it becomes way more clear what's going on. We can see what the population of certain frequency-range areas is. This kind of visualization allows us to better control the sound, especially if we are in the process of its shaping (recording, mixing, mastering, enhancing, …).
We have measurement devices for both cases. To observe the signal in time-domain we use an oscilloscope. This is an essential piece of equipment in the lab to observe the behavior of the signal in time. Even if we look at the complex signals on oscilloscope, we can determine if there's anything wrong with it: clipping, missing half-period, etc. We can see the value of amplitude very well, too.
Some oscilloscopes can be used as spectrum analyzers, devices that observe the signal behavior in frequency-domain, but usually this type of measurement tools are stand-alone (single purpose).
You might be more familiar with spectral analyzers that are part of the hi-fi system, most often part of the graphic equalizer. On digital devices this is a very common in-built feature, too, whether on music computer software or portable players.