Basically regenerative braking is re-capturing the kinetic energy from vehicle motion and converting it into another type of energy. Most commonly, we see kinetic energy converted into electricity to recharge the car's battery. In pure EV's, regenerative brakes are necessary to range and getting the most out of each charge.
When you apply the brakes, traditional brake pads bite down and let the kinetic energy dissipate as heat. Hybrid and electric cars can reverse the flow of power through their electric motors backwards to slow the car down. In a convenient engineering coincidence, electric generators and electric motors are one and the same. Friction and other energy losses still occur meaning that not all the energy is re-captured.
F1 teams use another type of regenerative braking system called KERS. KERS (kinetic energy recovery system) uses batteries or a flywheel to store the braking energy for later use. Whether or not KERS ever makes it to production vehicles depends on how the safety concerns are dealt with on the track. Motorsports have traditionally been the testing grounds for future road going tech, so any advancements made in either F1 or LeMans have the potential to influence future vehicles for sure.
Regen brakes are not without complications. Most hybrid and electric vehicles use electronic brake control units far more advanced then the average car. Blending friction and regenerative braking add another potential failure point to an imperative safety system.