Phase response reveals how a system shifts the timing of different frequencies. An ideal system has flat/linear phase response — all frequencies arrive simultaneously. Real-world systems (speakers, filters, rooms) have non-linear phase response, which can smear transients and blur imaging.
In speakers, phase response is closely related to frequency response — minimum-phase systems have phase shift determined by their frequency response. Crossover filters are the main source of phase deviation in multi-driver speakers. Time-aligned speakers (like coaxial designs) minimize phase issues at the crossover point.