Well, here's an example of using synthetic data to train AI. You want an AI to drive your car, you need lots and lots of data showing a car being driven (with associated info like braking, steering, etc) to teach it how to drive. You can use computer simulations of cars driving in different road conditions with different signs etc to build up the training data. Add some disaster scenarios (road collapse in front of you, a deer jumps out in front of you, etc) and do monte carlo excusions on them (i.e. simulate them thousands of times) so the AI sees what seems to work and what doesn't.
There are many other use cases for synthetic data.