A music tech student asked me what the difference is between analog and digital recording and mixing. I came up with a nice concise answer, and I thought I would share it here.
All microphones are analog. They convert pressure waves in the air into electricity, by having the air shake a little piece of metal, thereby generating a fluctuating electrical current. Mics differ in the specific ways that they do this. In dynamic mics, the air vibrates a magnet that is wrapped in wire, producing a current. In condenser mics, the air vibrates a metal plate that's part of a capacitor, which changes its capacitance, thus making an existing current fluctuate.
The analog/digital split comes into play when you're figuring out how to record the current coming off of the mic. In analog recording, the current changes the orientation of little magnetic particles embedded in the surface of a tape. In digital recording, the computer takes lots of very fast readings of the voltage on the wire (typically every 44,100th of a second). The computer stores its readings as an extremely long list of ones and zeroes.
To play back your analog tape, you run it over a magnet. The little magnetic particles in the tape produce a fluctuating current in this magnet which then gets sent off to the speakers. Ideally this current fluctuates in the same way as the one that you recorded off the mic in the first place, but you also pick up some noise and harmonic distortion along the way. In the speakers, the current agitates yet another magnet, and that magnet's vibrations drive the vibration of the speaker cone. The speaker cone, in turn, vibrates the air.
To play back your digital audio file, the computer sends its long string of numbers to a voltage generator, which sends corresponding electrical pulses down the wire to the speakers. These pulses reconstruct a fluctuating current that isn't quite identical to the one you put in, but it's very close, often closer than what analog systems can reproduce.
Typically, you aren't just recording from one microphone, of course. You can combine the currents from lots of mic inputs into a mixing board, which lets you cut or boost them to change their volume levels. You can also apply effects by modulating the currents in various ways. The mixer might be analog (a big complex collection of transistors and capacitors and resistors and so on) or digital (a computer program that mathematically models a big complex collection of transistors etc.)
It's possible to send the mic signals through an analog mixer to a digital recording device, and it's possible to send the signals through a digital mixer into an analog recording device too. Usually, both the mixer and the recording device are digital, because digital is cheaper, easier, more reliable, and sounds better unless you are using very high-end gear. However, sometimes people do like to use analog mixing and/or recording, because they want to add a little noise and harmonic distortion to the signal. Of course, there is nothing stopping you from adding noise and harmonic distortion using your computer, and plenty of people do exactly that.