In a recording studio/on recording equipment (not to be confused with "cue"):

"Q" stands for the bandwidth affected by a particular piece of equipment, usually an EQ unit or synthesizer. In other words, it's the span of frequencies, in octaves, around the central frequency that will be boost or cut. Higher end EQ units will have an adjustable Q.

For example, if you have a graphic EQ, and you boost 4 kHz 6 dB, typically (it could be different for particular units) this boost will effect one octave on either side of the center frequency (4 kHz).