Whether it's for performance or economy depends on how it's tuned and how the engine is sized relative to the equivalent pure gas car. The attractive things about these mild hybrid systems is that they're cheap, they don't weigh much (so you're not hurting efficiency by hauling around a bunch of batteries and electric motors), and they give you a lot of what a full hybrid (non-plug in) offers.

If you're not plugging in, you don't need a big battery, because the hybrid only needs to store the energy from braking, and then deliver it when the car speeds up again. Even though the motor is only 21hp, it provides a lot of low-end torque, which lets you have good acceleration from a stop. This is something modern efficient gas engines are generally bad at, and the immediate acceleration in a lot of modern cars is even worse because of aggressive upshifting to save fuel. The electric motor papers over this deficiency, so you can be more aggressive about using a smaller engine with less low-end torque. The electric motor is also much more powerful than a normal starter motor, so it allows the car to more aggressively shut off the engine at stop lights and even when coasting, and turn it back on very quickly.

I buy what you are saying but that particular gas engine is 330 HP.

At one particular RPM.

48 volt is what the industry calls mild hybrid. It allows for much better stop-start systems, which automakers get points for on EPA and European emissions testing.

It also allows for 48 volt super-charging and e-assist turbo, as well as a small amount of actual propulsion power (for instance to both start the engine and start the vehicle moving from a complete stop after the stop/start system has been engaged).

All of these systems fall under the term "mild hybrid".

A basic lack of fundamental understanding has caused the author to quickly fall into an expertly laid trap by marketers that seek to equate 48 volt systems with some sort of "green, hybrid, clean" spirit, leading to such bizarre statements like "The advantages of the new 48-volt systems are considerable. They offer fuel economy improvements of up to 15 percent"

Of course it's all about saving a few dollars on copper.

The main advantage of a hybrid system is that the engine can run at a more efficient speed, which is independent of the power being delivered to the wheels. Say you are driving through a town, accelerating from stopped to 30mph then cruising in traffic, the engine will start shortly after you start to move, run at 3000rpm the whole time (or whatever is the most efficient speed), then cut off when you begin the cruise.

This is why automatic transmissions now often have 7 or more gears, as it allows the engine to run at a more efficient speed. A hybrid system in comparison is mechanically a lot simpler though: In a Prius the clutches, transmission and alternator have all been replaced by a simple mechanical device with fixed gears and two electric motors.

As for the battery the Prius has a 1.3kWh battery, but due to battery longevity (the system tries to keep it charged around 60%) only around 400Wh is actually available for use.