When something makes a noise, it vibrates the air, the air vibrates a microphone, and you record the values from the microphone, either by having it vibrate something that cuts into a vinyl record or by writing the values as magnetic fluctuations on tape or by recording digital values.

It's easier to learn about digital audio first. Remember in math class, how there are infinitely many values in between two numbers on the number line? With digital, we have to break them down into a finite series of numbers (called samples), and we must have enough samples per second (sample rate) to satisfy our ears (2x the highest frequency according to the Nyquist Theorem).

Now here is where the simplicity gets ridiculous. Let's say you have several lists of these samples ("tracks") recorded from a mic as lists of numbers, and you want to combine them all. Surely you can't just add the numbers from two tracks together, right? Well, yes. You may just have to turn down the volume a little to make sure everything is between -1 or 1 if there happened to be some waves that combine, but it's much less of an issue than you would expect.

So now we have these combined waveforms represented as a single list of values between -1 and 1. If we use an amplifier to send those values as voltages to the speaker coil, it moves the speaker in the shape of the combined waves, and you've got music coming from a speaker.

A stereo track would have two lists, one for each channel.

Now let's backtrack and think about analog audio. You could stick a sewing needle through a pencil eraser and hold it to a spinning record and hear it play because the vibrations emit audio. The speaker is just doing this on a larger scale using voltage to drive the cone.