The term analog indicates that the audio signal is continuous rather than a non-continuous digital signal. Analog signals are considered to be the real-life version, producing a much warmer and natural tone compared to its digitized counterpart.
You will not find any computer-based components in an analog synth, the design is purely based around analog circuits and analog signals. These electronic sound waves are produced by what is known as a voltage controlled oscillator (VCO), VCOs are the heart of analog synths.
After the oscillator creates the signal, other electrical components can then be used to modify and alter the signal to create unique sounds. Due to the nature of these electrical components, the signal can become slightly distorted which gives it that natural and warm character.
There are three main circuits involved in producing analog sounds. These allow you to alter the pitch with the VCO, change the timbre with the VCF (voltage controlled filter), and adjust the volume with the VCA (voltage controlled amplifier).
Analog synthesizers have a long history but they first started to become popular amongst musicians around the 1970s. Moog designed a synth with a built-in keyboard and analog circuits, named the Minimoog, it became a huge success selling thousands of units.
The Minimoog paved the way for future synth units because it removed the numerous patch cables and introduced an arrangement called normalization, essentially connecting the analog circuits via switches. Synthesizers became easy to use and much more portable than before.
Digital synthesizers were introduced and became popular during the 1980s, they were capable of a wide range of sounds, compact and affordable, and pushed analog setups aside. They have a unique sound quality but they never matched up to the natural tones of analog.
Analog synthesizers are making a resurgence in the modern era, musicians and producers appreciate the warmer and natural sounds that they are capable of. Digital synths are flexible, but they are no match for the pure sounding analog circuit synths.