An isolation amplifier (also called a unity-gain amplifier) is an op-amp circuit which provides isolation of one part of a circuit from another, so that power is not used, drawn, or wasted in a part of the circuit.
This will be explained thoroughly now, because this may, at first, appear to be a daunting topic, but, in this article, we will break it down into parts, so that you'll hopefully understand in the end.
The purpose of an isolation amplifier isn't to amplify the signal. The same signal that is input into the op amp gets passed out exactly the same. This means that output voltage is the same exact as the input voltage, meaning if 10V AC is input into a circuit, 10V AC is output.
The purpose of an isolation amplifier is to isolate the circuit which appears before the amplifier from the circuit that appears after it.
Below is an illustration: