the resonance circuit is a tank circuit that consists of inductor, capacitor and whether the resistor or not which is tuned at some certain frequency called rhe resonance frequency
at this freq the impedances of inductor and capacitor become equal and cancel each other and then the equivalent ckt will be a finite resistance (because our l and c aren't ideal ) otherwise( if they are ideal!) the eq ckt will be short ckt ( if l and c are in series) or infinite ressistance(in parallel case ) .in both case the energy is circulated between l and c. we can use tank ckt's in many applications such as filters , oscillators and etc to picking up a certain freq(in narrowband applications) or certain bandwidth(in wideband application by some modifications). or in oscillators to generate a waveform with special frequency(oscillation freq).
