As an analogy, see the conventional water tap as an analog control, an electric light ON-OFF switch as a digital control. After the handheld Abacus calculator (low-power, durable, bio-degradable), Mechanical and electro-mechanical computers were made and studied, The very first electronic computers were Analog Computers using an opamp as a building block.
Operational Amplifiers
With a few Op-Amps and a regulated Power supply, many Instrumentation and Process control equipment can be designed. The Human Brain understands Numbers, Quantity and it regulation very well ! On the right you can see a analog controller based on opamps and discrete devices. A Heater, Fan and Motor is regulated, controlled and timed for a process.

Analog is about numbers, the circuits can be understood and designed mathematically or empirically. Designing and Building a True RMS Rectifier with Op-Amps, will help a designer digest many Op-Amp capabilities.
Analog Op-Amp Circuits