How do phase carries structural information about the function? Suppose you are on a railway platform and you hear the sound of train coming towards you. Now, Using Fourier transformation we can convert the time domain function (here take  sound as a function) into the frequency domain.
I have heard that location (structural) information of a function in the time domain is tightly coupled with phase information in the frequency domain. So can anybody help me to understand the above statement given in bold letters with the help of above example?
Also, can we find that whether train is coming  towards you or going away from you from the phase information of the sound function?
 A: You may consider reading about Aharonov-Bohm effect. This is one of those cases, where the phase of the wave function, in sum with the electromagnetic 4-potential, is extremely important, as it gives different physical results. This effect was also checked experimentally, so it is not a pure theoretical abstraction.
A: To keep things simple, let's talk about plane acoustic waves in one dimension.
If we solve the wave equation in one dimension , we find that the acoustic pressure as a function of space and time is of the form
$$P(x,t) = Ae^{i(kx -\omega t)}$$
where $A$ is the maximum amplitude, $x$ and $t$ are the displacement and time respectively, $\omega$ is the frequency, and $k= \frac{2\pi}{\lambda}$ is the wavenumber (where $\lambda$ is the wavelength). $i$ is the imaginary unit.
Notice that both the spatial and temporal variation of the acoustic pressure are information carried in the phase (the exponentiated term) , not the magnitude (amplitude).
Now let's talk about Fourier transforms. One can take a Fourier transform from the time domain to the frequency domain, or vice versa. In our simple example, there is only one frequency, but real sound is usually composed of a mix of frequencies (like human speech for instance). So the Fourier transform from the time to the frequency domain is key in understanding what frequencies a complex acoustic signal is composed of. 
But note something else. As is suggested by the exponential form above, we can equally well do a Fourier transform from the spatial domain to the wavenumber domain, or vice versa. And this fact, turns out to be key in analyzing the spatial structure of a signal in terms of the superposition of wavenumbers (which, remember, are related to wavelengths) found in that signal.
As just a simple example, imagine we wanted to make a line array of microphones that is sensitive to signals coming from a certain direction. It turns out that if we apply weight vectors to each microphone to "steer" it to a certain direction $\theta$, the solution looks an awful lot like the expression for a spatial-wavenumber Fourier transform:
$$
D(\theta) = \sum_{n=0}^{N-1} w_n \exp\left(iknd \sin(\theta) \right).
$$
where $w_n$ are the weights applied to each microphone, $n$ just is an integer that labels each microphone, and $d$ is the microphone spacing.
So to sum it up, the phase carries both spatial and temporal information about the signal, and the respective Fourier transforms carry information about the frequency structure and wavenumber structure of the signal.
