This is a brief and very general answer which points to some papers which deal with LIGO calibration in detail. More detailed answers might be possibly given on either point, but can easily cover complete books each easily, too.
A response or transfer function of a piece of equipment describes how the device responds to an input signal. This could be in terms of frequency, of photon efficiency, of spatial resolution / diffraction for an optical piece of equipment etc.
Mathematically the detected signal is the convolution of the original (unchanged) signal with the transfer function of the instrument. In order to obtain the original signal you have to know your transfer function and deconvolve the detected signal with the (hopefully measured and thus well-known) transfer function of your instrument.
In the case of these detectors the most interesting behaviour is the wavelength (or frequency) dependency of the sensitivity of the detectors, thus how well or easily we can detect a signal with a given frequency - possibly as a function of the direction of the signal direction with respect to the sensor orientation.
On the detailed calibration, thus establishment of this particular instrument's transfer function is topic of various works which took years to measure and establish. Some relevant papers on this topic might be these which discuss the sensor calibration prior to measurements - establishment of the sensor's transfer function is essential part of this:
