Radio transmission works by transmitting a carrier sinus wave, and then modulating (changing some properties) of that carrier with another signal, which is the information content. The frequency you tune in on your radio (i.e. 103.5 MHz) is the carrier frequency, the modulation is the sound content (a signal with frequency between 0–20kHz).
AM works by modulating the strength of the carrier wave, like this
The signal superimposed on the carrier frequency (i.e the strength of the sinus) is the actual sound content.
FM works by modulating the frequency of the carrier wave slightly, like this
The deviation from the carrier center frequency is what constitutes the information content.
AM is alot more sensitive to disturbance than FM (and thus produces lower quality sound in the presence of disturbance or low signal strength than FM). FM is on the other hand alot more robust towards disturbances.
That’s why AM is being left behind.