The lens achieves its flexibility thanks to a design that puts its electronics into isolated pockets linked by stretchable conductors. there's also an elastic material in between that spreads the strain to prevent the electronics from breaking when you pinch the lens. And when the refractive indicies all line up, you should get a lens that's as transparent as possible and largely stays out of your way.
The sensor in question is straightforward: an LED light stays on as long as glucose levels are normal, and shuts off when something's wrong. Power comes through a metal nanofiber antenna that draws from a nearby power source coil. That's about the only major drawback -- the low conductivity of the antenna means that you can't just tuck the coil wherever it's convenient.
This isn't a purely theoretical exercise, as co-author Jang-Ung Park explained to IEEE Spectrum that he expects a commercial version of the contact lens in 5 years. And the technology isn't just reserved for glucose monitoring, either. The soft electronics could also be used to deliver medicine, saving you the trouble of taking pills.