The quality factor is the measure of "selectivity" of an AC resonant circuit.
Resonant circuits are used to respond selectively to signals of a given frequency while discriminating against signals of different frequencies. If the response of the circuit is more narrowly peaked around the chosen frequency, we say that the circuit has higher "selectivity". A "quality factor" Q, is a measure of that selectivity, and we speak of a circuit having a "high Q" if it is more narrowly selective and "low Q" if it is less narrowly selective.