Resonance occurs whenever the phase angle of the circuit is zero, The only way that f = 0 is if XL = XC.
Generally resonance is achieved by varying the angular frequency w the circuit until XL = X C.
The importance of resonance is that the circuit can either absorb or dissipate the maximum amount of energy at resonance.
One practical example is used in a radio receiver. Many the frequencies from different radio stations are impinging on the radio's antenna at the same time. By varying the capacitance in a circuit (connected to the antenna) the circuit can be tuned so that the resonance frequency of the circuit is equal to the desired station frequency. The circuit then absorbs more energy from this impinging frequency than any of the other impinging frequencies.
The Q factor is used to measure how narrow or broad the band of frequencies are near resonance.
The last approximation is only valid when Q is larger than 2 or 3.
A large Q also means that the power absorbed or dissipate is also large.
At resonance, the voltage across the inductor and the voltage across the capacitor are the same at any instant but they are 180 0 out of phase with each other. They cancel each other out so that the voltage drop across RLC circuit is due to just the voltage drop across the resistor alone.
