To really explain an op amp you need to know a little about transistors, and a few clever ways of using them first.
To explain without knowing about transistors, an op amp is a chip.
It can come with 1 op amp on a chip or a few.
An op amp requires a power supply.
An op amp has 2 inputs called inverting input and non inverting input.
An op amp has one output
An op amp will mutltiply the difference in voltage across its inputs by around 200,000 and the result will be its output.
Obviously unless your input difference is very small the output will be saturated and go to either fully positive or negative. (ie nearly 15V or - 15V in my sketch)
This kind of gain is pretty useless as it is, due to distortion
Something called negative feedback is used to reduce the gain to a much smaller amount and this makes the op amp have extremly low distortion.
Negative feedback is obtained using resistors (see diagram)
Note the power supplies are not usually shown
Typically you keep gain to less than a few hundred.
Notice inverting amp gives gain and inverts polarity
non inverting amp just gives gain
gain = vout/vin ie 10 gain = 10x voltage in is outputed. But op amp can only output to close to its power supply.
An op amp has extremmly high impedance in the noninverting amp and reduced impedance in inverting amp due to the feedback resistors. Impedance can be seen as if you supply a voltage, what current is conducted. High impedence = low current
I used this site that has cool little models you can input variables in and see the result to learn about op amps.
ElectroSim: Electronic Circuit Simulations