What is an op-amp?

It is so named because it was developed for perform arithmetic operations.  Amplifiers, buffers, comparators, filters, etc. can be implemented with simple external circuits.
An op-amp has five terminals: positive power supply, negative power supply (GND), noninverting input, inverting input, and output. Generally, these terminals are named as shown below. (Positive and GND terminals may be omitted from the symbol of single-supply op-amps.)

An op-amp amplifies the difference in voltage between the noninverting (IN(+)) and inverting (IN(-)) inputs. Its output voltage is given by Equation 1, which indicates that the output is in the same phase as V_IN(+) and in opposite phase to V_IN(-). 

V_OUT = A * ( V_IN(+) – V_IN(-) )         (1)

In the basic form of usage, an op-amp acts as a voltage amplifier or a comparator. It can also be configured as a filter, phase shifter, buffer (voltage follower), etc. Nowadays, op-amps are commonly used to amplify weak analog signals from sensors in a wide range of IoT devices and home appliances.
Op-amps are generally used with negative feedback to reduce product variations in gain and expand the bandwidth. Typical applications of op-amps include noninverting amplifiers, inverting amplifiers, and voltage followers, which are configured as shown below: