what is the definition of quality factor

Q factor or quality factor of a tuned circuit is defined as the ratio of the reactance to the resistance of the circuit. 

It is in general given by,

So, for an LR circuit the quality factor is given by,

Where, f is the resonant frequency.

And for an RC circuit, 

It is also defined as the ratio of the total energy to the energy lost per cycle in the circuit.

The importance of Q factor is: The Q factor determines the sharpness of the resonance curve, higher is the Q sharper is the resonance curve. This also means higher is the Q factor of a circuit lesser is the loss in energy of the circuit.