The radio station generates extremely stable waves in the radio frequency range. This range permits more power to be generated & contained in the waves than do sound waves, so the signal goes a long distance. We can create a radio wave generator with power to send signals to the edge of the solar system. Also, radio waves are a very-much higher frequency than is sound.
The radio (receiver) to which you listen has a circuit which tunes itself (with your help in selection) to the signal broadcast at the radio station. When your receiver's circuit is exactly tuned to the broadcast signal the sound which comes out of the speakers is absolutely nothing - no sound. They are in harmony and so, the sound doesn't exist, is not produced.
Then, the broadcast station messes with the broadcast signal on purpose. The variation exactly matches the much slower, lower frequency modulations that sound expresses, and sends these variations out on its signal. This requires very good and expensive equipment.
The receiver's circuitry does not change, and these modulations cannot be followed. They become irritations to the circuitry, and so it spits them out into an audio amplifier circuit, which drives the speaker/headphones.
The broadcast radio waves are called the "carrier wave" because they carry the information, but are not part of the information. The information (music, voices - even rap) is called the modulation wave, or a couple of other names, depending on what features are of focus.
AM radio is 'Amplification Modulation", where the audio signal increases/decreases the power output slightly to follow the sound. FM is Frequency Modulation, which tweaks the output frequency slightly to track the audio.