The advantage, as the name implies, is the range. While fully electric vehicles need to charge their batteries and are therefore limited to the charge a battery can hold, a REEV generates its own power. It only has to carry enough batteries to carry it for a little more than the average distance of a journey, rather than having a much larger contingency capacity for rare longer trips; this reduces the weight of the car dramatically and also, because of the high cost of batteries, keeps the price down.
Moreover, because a REEV’s engine is only charging a battery, it can always run at its most efficient speed; it doesn’t have to generate a variable load, high under acceleration, low while cruising, like an engine that is directly driving a car. If you have to burn fuel to drive a vehicle, REEV proponents argue, then this is the most efficient way to do it.