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Wiktionary
q factor

n. a measure of the quality of an electric circuit; the ratio of the reactance to the resistance

Wikipedia
Q factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, and characterizes a resonator's bandwidth relative to its center frequency. Higher Q indicates a lower rate of energy loss relative to the stored energy of the resonator; the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one. Resonators with high quality factors have low damping so that they ring longer.

Q factor (bicycles)

The Q Factor of a bicycle is the distance between the pedal attachment points on the crank arms, when measured parallel to the bottom bracket axle. It may also be referred to as the "tread" of the crankset. The term was coined by Grant Petersen during his time at Bridgestone Bicycles. The "Q" stands for "quack", a reference to the wide stance and waddling gait of ducks.

Q Factor is a function of both the bottom bracket width (axle length) and the crank arms. Bottom brackets axles vary in length from 102mm to 127mm. Mountain bike cranks are typically about 20mm wider than road cranks.

A larger Q Factor (wider tread) will mean less cornering clearance (while pedaling) for the same bottom bracket height and crank arm length. A smaller Q Factor (narrower tread) is desirable on faired recumbent bicycles because then the fairing can also be narrower, hence smaller and lighter. Sheldon Brown said that a narrower tread is ergonomically superior because it more closely matches the nearly-inline track of human footsteps.

Though it seems intuitive that a narrower tread is superior since a walking person must put their foot more to the centerline of the body to balance, this is not the case when pedaling a bicycle, where the "steps" are so very close together and balance a non-issue.

Scientific research has emerged from The University of Birmingham in the United Kingdom that shows narrower Q Factors are more efficient, likely due to improved application of force during the pedal stroke, as well the potential for reduced knee variability and risk of injury.