Here's an example of how hybrid operations improves FE. Attached are 2 charts for the Prius 1.8 liter engine. The second is a BSFC curve which shows torque and rpm on and superimposed are Brake Specific Fuel Consumption Curves. The units are grams/kWh of fuel consumed at specific rpm and torque. The goal of hybrid operation is to improve the operating characteristics such that BSFC moves from a high number to a lower number for the same rpm. What you will notice is that at a fixed rpm, ICE can operate at different efficiency based on the amount of torque which it supplies. So, what the hybrid algorithm does is to increase ICE torque from the base torque needed to propel the car. The increased ICE torque is used to generate electric power which can be stored in the HVB. In addition, the fuel used by doing this decreases in g/kWh for propelling the car. So, torque required to propel the car hasn't changed but fuel to propel the car is less. Now, fuel is needed to supply torque to the generator but it is at a very efficient BSFC point. There are losses in converting the mechanical power to electrical power for storage and reuse. But, the overall gain in efficiency via hybrid operation is positive resulting in increased FE. Of course the greatest benefit is when EV is used on initial acceleration from a stop so that ICE can be shut down. ICE is very inefficient for use on initial acceleration from a stop. In essence, energy stored in the HVB when ICE ran very efficiently replaces the energy that would have been required using ICE to accelerate from a stop. This nets a fuel savings. The same happens on highway cruising especially if ICE torque is very low and EV can be used instead.
The first "colored dots" graph shows actual operating data. Assume engine rpm is 2000 rpm and torque is 60 (likely going down a grade) as this is not an efficient operating point. The algorithm can spin the generator to maintain the 2000 rpm need to keep speed constant (negative split mode). Lets's is the generator can add 400 effective rpm to the output shaft and ICE rpm can be reduced by 400 to 1600 rpm. The ICE is still supplying 60 Nm of torque. So, now ICE efficiency has improved somewhat but still not very efficient. But since we have a HVB with room to store additional energy, rather than operate in negative split mode the algorithm operates in positive split mode by increasing load on ICE by generating electricity with the generator. Engine rpm will have to increase from 2000 rpm somewhat say to 2400 rpm and assume the generator is consuming 30 Nm of load. ICE is now operating in the "cyan dot" at 2400 rpm and 90 Nm or the most efficient region of the BSFC.