if you take some system, for it to faithfully reproduce the input signal, then all signals traveling through it must have the same delay time. if the time varies for different frequency components, you get ringing on the edges of pulses. A constant time delay means that the phase delay varies as what is a 5 degree delay at F1, is a 10 degree delay at 2 X F1, 15 degree delay at 3 X F1. . . Group delay is much more useful it is the time for a group of frequencies to get through a system and might be specified for a video system as +- 10 nS, 0 to 5 MHZ, then +20 -50 nS 5 -10MHZ.
Group delay meters, modulate a low frequency on to a carrier, the modulation is typically 100-300 KHZ, and the carrier is swept 0 -10 MHZ. This swept and modulated carrier goes into the system. The output of the system has the phase of the demodulated modulation compared with the original modulation, so as the frequency is swept a display results linking the swept frequency to the phase difference of the input and output modulation, but as this is a fixed frequency it is calibrated in nano seconds.
Frank