Though technically more complex than this, Damping factor is usually thought of as an indicator of how tight an amplifier will sound when powering bass speakers. A speaker's driving motor is a coil of wire (called a voice coil) mounted within a magnetic field. As this coil of wire moves within the field a voltage will be induced in the voice coil. If resonant motions of the speaker are not sufficiently short circuited by the amplifier, the speaker output can have an over accentuated or "boomy" bass sound.
From a technical measurement stand point, Damping factor is the ratio of the rated speaker impedance to the amplifier's output impedance. Low output impedance is the consequence of the amplifier having substantial negative voltage feedback taken from its output terminals. Properly designed negative feed back not only corrects for output voltage errors induced by the speaker but also produces other benefits: