Why is it required in radio receiver to tune the LC circuit to the the resonant frequency of the station in order to receive the station ? How this tuning filters the desired signal from the other signals. Can anyone explain this to me please ?
The L-C filter used to tune to particular radio stations has high Q. Put another way, it passes only a narrow notch of frequencies. When the notch-pass filter is tuned to a particular frequency, it will pass that frequency but heavily attenuate others. Radio stations are spaced far enough apart in frequency so that the signals for other than the desired station are attenuated to below the "don't care" level.
Tuned LC circuits actually have several roles in a typical receiver.
One is as a preselector - basically what Olin described, where the filter is tuned to pass one desired station's frequency and attenuate all the others. However, this is not typically as sharp or precise as desired to select only a single station from the band.
Modern receivers are heterodyne based - they effectively "go out and grab" the signal of interest, and move it to a fixed "intermediate frequency" where a fixed frequency filter can more specifically pass it and block adjacent channels. Often the IF filter uses other mechanisms than an LC resonant circuit, but it is typically surrounded by some LC circuits, possibly in the form of transformers with adjustable ferrite caps. The IF is typically also at a lower frequency than the signal of interest, and the bandwidth of a filter tends to scale with its frequency, so a filter built for a lower frequency is more easily made sharp.
To "move" a signal it is necessary to use something called a mixer which can subtract (or add) the frequency of a Local Oscillator with the input frequency. So a tunable oscillator is built with an output that differs from the desired receive frequency by the intermediate frequency. A simple way of building a local oscillator is to build an oscillator tuned by a variable LC circuit, typically a fixed inductor and a plate capacitor connected to the tuning knob. If a preselector is used, it is often tuned by an additional variable capacitor stacked on the same shaft.
A broadcast AM receiver typically converts to an IF of 455 KHz, filters there and demodulates there. In contrast a broadcast FM receiver will typically convert to a first IF of 10.7 MHz, filter there, then convert with a fixed second LO to a second IF of 455 KHz for demodulation. One type of FM demodulator requires making a second copy of the signal with a phase shift, which can be accomplished by an LC circuit tuned to do that to a 455 KHz signal.