Playing a pcm file through a speaker with arduino
You are right that the values in a wav file are amplitudes. 16 bit signed values to be precise.

And that amplitude is just a voltage. Negative values are normally a negative voltage, but they don't have to be. They can be just a voltage below a pre-determined mid voltage around which the wave swings (known as a DC offset).

To play the waveform you just have to generate the corresponding voltages at the right times. That is usually done using a timer so you get the frequency right. For instance a 44100Hz file has to have a sample voltage generated 44100 times per second. 44100 samples will be a sound clip lasting 1 second.

But of course the Arduino cannot generate a voltage, so instead PWM is used instead. Filtered through a low-pass filter it turns into a voltage. It also uses 50% duty cycle as "zero" for the waveform, which is scaled to fit into the resolution of the PWM.  The PWM has to be running at a considerably higher frequency than the sample frequency of the waveform so it has a chance to represent a voltage before it is asked to change again.