A parameter used in electrical engineering to, essentially, describe the amount of resonance in a filter circuit; higher Q corresponds to more resonance. In a bandpass filter, higher Q corresponds to a narrower pass band. In a low pass or high pass filter, higher Q creates an emphasis (boosted response) at just below/above the cutoff frequency.
In synthesizer and other audio filter circuits, higher Q is achieved by increasing resonance. A few studio audio products have bandwidth controls marked with Q values, but since the Q value is a ratio of several factors, it has no immediately obvious connotation to a non-mathematician. Resonance controls on synth filter circuits are usually marked in arbitrary units.