Op-amps (and buffers made with op-amps) are actually pretty ubiquitous in real-life circuits. We will be seeing more about them and applications of them towards the end of the course. An op-amp is a kind of basic amplifier (and a buffer is a unity-gain amplifier). There are many reasons you might want to increase the voltage amplitude in a circuit. A canonical example is a sound-amplifying circuit: when you turn up the volume on a music-playing device, you are increasing the gain of an amplifier. An example from my own field of physics research is an amplifier that turns tiny signals from particles into more robust signals which are easy to digitize. In practice, amplifier frequency response matters quite a bit, as you often want to suppress noise or shape a signal in a particular way.
Buffers are commonly used to avoid loss of amplitude when connecting one device to another (as we saw in the example of sequential filters).
Real life op-amps have a lot of imperfections, and actual circuits will usually use op-amps together with other circuit elements in clever ways to achieve specific performances.