Nike Hindsight is, put simply, like giving bicyclists a pair of bifocals for their peripheral vision. By using Fresnel lenses on the sides of eye wear, riders can detect motion in a field of view beyond the normal human limit of 180º. To get technical, high power, diverging Fresnel zones aligned vertically distort into view an extra 25º of view on either side. In doing this, vision is radically distorted in the periphery, but as the eye detects only motion in that area, little clarity is lost in the process.
A rider's clear benefit is in the early warning of approaching vehicles, but a less obvious advantage is reducing the necessary head rotation to check completely behind oneself. Moreover, while the project was directed towards bicycling for the sake of simplicity, there's a myriad of sports and activities where a greater field of view becomes an advantage, so feel free to speculate.