If your name is on the insurance policy and your age allows it, then you are covered. If your name is not on the policy and you get into an accident with your parent’s car, the car is covered in most cases. This is because the insurance covers the car, not necessarily the driver. Again, it would depend on the specifics of the insurance policy.
In some policies, the policy holder is given a considerable discount as a safe driver but anyone who drives it must also have that same safe driver rating otherwise the insurance will not cover for any damages or injuries. If this is the case with your parents, then you are not covered unless you have the same 10 year road star rating.