Why In a common collector (emitter follower) stage the load sits in the emitter leg, so the emitter voltage tracks the base voltage about 0.7 V below it. The output therefore follows the input with voltage gain just under 1 and no phase reversal, giving in-phase input and output. Its value is impedance transformation: high input impedance, low output impedance, and useful current gain, which makes it a good buffer or driver stage.
Watch out The choice pairing low input impedance with phase inversion mixes up two other configurations: the common emitter inverts the signal, and the common base is the one with low input impedance and no inversion. Differential inputs describe an op amp or long-tailed pair, and the OR-circuit answer is digital logic, not an analog amplifier stage.
Emitter follower: the emitter FOLLOWS the base, so it stays in phase, gain about 1, high Z in, low Z out.