IRF stands for Instrument Response Function. The IRF is the best approximation to a temporally infinitely short process possible to measure with a given instrument. A synonyme sometimes used is 'lamp function', which stresses the fact that the temporal profile of the excitation is the most intuitive contribution to the IRF. Of course, the temporal resolution of all components of the instrument contribute to both shape and width of the IRF. The observed decay in a time domain measurement is a convolution of the 'real' decay with the IRF.
see also How To Measure the IRF