Protection diodes in an audio amplifier
The LM386 looks internally similar to the LM380, which you can see more about here on EESE. The difference voltage between the two inputs should never be allowed to exceed a certain amount because once it does, the inputs will sink/source a great deal of current as the internal BJTs go into full saturation. The difference should be kept well below a volt and if you read the datasheet you will see, under absolute maximum ratings, that the difference should be kept within \$\pm400\:\text{mV}\$ of each other.

The assumption made in the circuit is that the 1N4148 diode doesn't get involved until the signal (relative to ground) well exceeds that limit. So the belief by the designer is that they only protect the opamp's input and have no other effect. That's wrong, though.

First off, many input sources will provide twice that peak value of signal (or more, on occasion.) I usually plan on \$600\:{\text{mV}_\text{RMS}}\$ and may decide to plan on more than that. (The peak will be \$\sqrt{2}\$ larger.) The solution the designer may point to is the potentiometer. Just set it to midway and you are fine, the designer may say. Okay. Sure.

But the 1N4148 will conduct substantially (when taking into consideration the potentiometer value) at \$400\:\text{mV}\$ (and less.) I would expect at least \$10\:\mu\text{A}\$ and perhaps as much as \$30\:\mu\text{A}\$ in that case. With the potentiometer at midpoint (per above argument) another \$2.5\:\text{k}\Omega\$ of source impedance has been inserted. This is a drop of perhaps \$50\:\text{mV}\$. So, say the input peak is \$800\:\text{mV}\$ and the potentiometer cuts this down to the maximum input difference (already meaning some amplifier distortion is likely) of \$400\:\text{mV}\$ peak, then another signal-dependent \$50\:\text{mV}\$ is dropped by the potentiometer. Which means the signal is further distorted by the diode presence.

So, yeah. It's protection. They conduct pretty hard (more than a milliamp by themselves) if the input exceeds \$600\:\text{mV}\$ peak, for example. But it's also going to increase signal distortion if the input requires the use of the potentiometer and they add some loading, regardless.