What is a car stereo system composed of?
There are many things that go into a stereo setup, 
but they can be broken down into their basic components:
Source
The source is where your music comes from. This can be in the form of a CD, mp3 player, cell phone, etc. Basically what the music is stored on.Signal Processor
For your music to play through the speakers, the signal first has to be processed. For CDs the signal processor is built into the CD player. For phones and mp3 players, the signal processor is usually built in to the phone/player itself. A signal processor takes the digital signal from your source and transforms it into something the amplifier will understand so it can be turned into sound.
Amplifier
After the signal is processed, it is amplified by either an external amplifier or the radio. Most head units are both a signal processor and an amplifier in one. This makes it easy to install aftermarket radios into otherwise stock cars since most cars have a basic radio with an amplifier built in. So really a head unit does both of these steps.
You can also add an external amplifier for cleaner and/or louder sound. This takes the signal from the radio or other signal processor in more advanced setups and amplifies it before sending it to the speakers to produce sound.
Speakers
Finally, the amplified signal makes its way through the speakers in the form of sign waves which produces the sound you hear that we call music (some better than others).
How Does My Car’s Stereo Work?
Most Factory Systems
Most cars come with a basic all in one head unit that acts as the signal processor and amplifier that sends that signal straight to the speakers. Since the signal processor is built into the cheap head unit, you usually can’t get good quality sound out of the factory setup without adding fancy external processors.
Amplified Factory Systems
Amplified systems are meant to sound good from the factory, but most of the time they don’t, and this usually complicates things. The way these systems work is the head unit acts as the signal processor that sends that signal to an external amplifier then to the speakers. Since these are meant to sound better than the all-in-one head unit setups, they usually do once you start adding your own components as well. But in some cases they end up sounding worse and expensive signal processors come into play.