A microphone is a membrane attached to a means to generate electricity (like shaking wires around a magnet). When you make sound by a mic you shake the membrane and it in turn generates a small amount of electricity.

This electricity is an analog signal (it's continuous, and the exact amount changes over time). We can take that signal and digitize it (literally chop it up into distinct digits) by using an ADC or analog to digital converter. Essentially an ADC takes a snapshot of the analog signal at a specific point in time, and repeats that snapshot process very quickly. If you take enough snapshots fast enough you can have a reasonable approximation of the original signal (like following a dotted line).

Now we have a digital signal and we can store those series of snapshots in a file.

But how do we turn that back into sound? We literally just follow the process in reverse.

We open the file and get the list of snapshots. We pass those to a DAC or digital to analog converter that generates a continuous analog signal that passes through every original point. We pass that signal to thin wire wrapped around a magnet and attached to a membrane. This mechanism takes the small generated electric field from the DAC and causes the membrane to shake in the same pattern that the mic originally shook in.

In practice there are often other steps in line such as amps to increase the strength of a signal or compression to minimize how much space the snapshots take up.