Damping factor (DF) refers to the ratio of internal impedance of the amplifier to the speaker system. Simply stated, the DF is the ability of the amplifier to allow the speaker cone to return to its mean static state as soon as possible, from the momentum generated from a singular pulse. So, if the amplifiers damping factor was very low, the speaker cone would oscillate about its mean static position before it came to a standstill. This then adds colouration to the sound field, which is undesirable.
On the other hand, if the amplifier's internal impedance is high, the speaker cone would encounter resistance on rebound and then continue to bounce about its static mean position until it finally comes to rest. The amplifier then acts like a trampoline for the speaker cone... perhaps desirable for those who like boomy bass, but less desirable for those who want precision. An amplifier with a high damping factor (greater than 20 DF), is able to absorb the energy generated by the cone rebound, and thereby allows the speaker to return to its mean static position as quickly as the speaker design will allow.