The quality factor (Q) applies to any resonant circuit component; most often the quality factor of the coil determines the overall Q of the circuit.
Inversely related to the fraction of the energy in an oscillating system lost in one oscillation cycle. Q is inversely related to the range of frequency over which the system will exhibit resonance.
In a parallel tuned circuit (such as used in a MR coil), the quality factor is defined as:
Q = vL/R
where L is the coil inductance, R is the circuit resistance, and v is the angular frequency. Increasing quality factor results in improving the signal to noise ratio SNR by a factor √Q and also produces a sharper frequency response (decreased band width). The Q of a coil will depend on the circumstances under which it is measured, e.g. whether it is 'unloaded' (no patient) or 'loaded' (patient).