Automatic volume control (AVC) in radio was first introduced in radio's circuit design the early 1930's to help regulate the sound level when searching for a station. It was not a common part of radio circuit design until the mid-late 1930's. Some of the early circuits were complex and pretty much ineffective. The common accepted method for most radios was standard by 1939.
AVC works by regulating the incoming radio signal, not your listening level. Without going into too much technical language, I'll first comment on how radio's worked before AVC - in a word, poorly!
The earliest methods of controlling the volume level of your radio was by a myriad of controls, some regulated how much power you fed to the filaments of the tubes. If your radio had 4 tubes, you may have had 4 controls just for the purpose of how bright you burned the tubes! If there were 6 tubes, 6 controls may have been there plus a bunch of other dials to twist and fiddle with. It was not easy to find and tune in a radio station in early - mid 1920's.
How does AVC help? Without it, depending on where you had your control/s set, strong stations could be easily found but the controls had to be advanced upward to find the weak ones. Then should you tune onto a strong station the sound would blast out! AVC works by sampling the signal strength of the amplified signal that comes into your radio at a specific point before you actually hear it or adjust it. If the signal is from a strong local station, the detecting circuit senses a large signal and tells the amplifying circuits at the prior stages to reduce amplification. If the detecting circuit senses a weak signal, it does just the opposite, it increases the gain. This way (except for extremely weak stations), the volume level that you control is pretty uniform throughout the dial.
Since radio stations vary in quality of sound (some often exceeding 100% modulation) you will still hear some variations in listing level of some station because of over (or under modulation). Any sounds over 100% modulation will be distorted.
What is modulation you ask, well that is the amount of audio signal riding on the radio station's frequency carrier. Now what is frequency and what is carrier - we are getting too technical for now. I may have more on these subjects later if there is any interest among you none technical folks. The carrier signal (converted to an intermediate frequency or IF) is what is used in a modern AM super-heterodyne radio to develop the the AVC control voltage.
I often add an AVC circuit as part of my restoration of some of the early (more primitive) receiving circuits. I do this by carefully concealing (to maintain original appearance) the needed additional components inside the RF & IF cans and a small package that looks like an early condenser block (see example).