Why is this circuit isolated?
That is not a very good illustrative diagram, and it's copied directly off the IL300 datasheet: 

Here is how it should be connected: 



The LED has an output that varies with temperature and decreases with time, whereas the photodiodes are quite stable with time and will track each other well. So one photodiode is used in a feedback loop to control the LED brightness, and the other responds similarly on the other side of the isolation barrier. 

As the LED decreases in efficiency, the feedback loop will increase the LED current to maintain similar emitted light, which is seen by both photodiodes. The photodiodes are in reverse bias.