Why At resonance the inductive and capacitive susceptances cancel, so the L and C branches together draw no net current from the source. What is left is the resistive element, so the circuit's impedance is purely resistive and equal to that resistance. This is the maximum impedance a parallel RLC circuit can present, the opposite of a series resonant circuit, whose impedance drops to a minimum equal to its resistance.
Watch out Saying the impedance is high compared to the circuit resistance is tempting because parallel resonance does give a high impedance, but it is high compared to off-resonance values, not compared to R itself; it equals R.
Series or parallel, at resonance the reactances cancel and Z = R. Parallel peaks at R, series bottoms out at R.