Impulse function is a signal that contains information for all frequencies from 0 to infinity. Since it contains this information, we give this as input to the headphone. The headphone then gives an output (which the OP posted). Now, we transform this output from time domain to frequency domain to see the frequency response of the headphone.

Omegalol. There's no way of measuring FR "directly". See my comment in the main thread to learn how frequency response is computed and what Impulse response actually means. FR is calculated from impulse response only.

Can you explain what you mean by "time delays do not alter frequency domain". A delay in time domain causes a phase shift in frequency domain. So it does alter the Fourier transform.

No, impulse response is the time domain counterpart of frequency response. They both convey the same information but in different domains. See my comment in the thread for a more detailed explanation.

Clearly you have no clue about signal processing. The frequency response (which is one of the only relevant measurement according to you) is actually computed from the impulse response by applying Fourier transform and selecting its magnitude.

OP wanted to know about impulse response, not step response.

Impulse function, δ(t) is defined as function whose value is infinite at t=0 and 0 elsewhere. So, Impulse function can be thought of as a signal which has a uniform amplitude of 1 throughout the frequency range. We give this signal as an input to the system (headphones) to find it's response for all the frequencies. The output given by the system is called the impulse response (the plot you posted). Now, if you compute the Fourier transform of the Impulse response, you'll get a complex function. The magnitude of this function is the frequency response of the system. Audiophiles are usually more interested in the frequency response than its time domain counterpart.