AM modulation is the process of encoding a information frequency into a carrier frequency. By adding then multiplying the two together, the carrier peak voltage is adjusted by the amplitude of the information signal.
This circuit uses a biased diode to provide nonlinear modulation. An LC circuit tuned to the carrier afterwards both adds the bottom half to the rectified signal, as well as acts as a bandpass filter to filter out the harmonics (Vm, 2 Vm and 2Vc) that are produced from the modulation.
The drawback to using a diode as a modulator is because of its low forward bias, this can only be used on small signals in the millivolt range.