The key was a high concentration of salt that produces the same protective layer on electrodes (a solid electrolyte interphase) you'd get out of a conventional electrolyte, preserving the electrodes and letting the battery hold more energy.

There's one main problem right now: batteries with these watery electrolytes don't last very long. They hold out for just 70 cycles where many conventional lithium-ion batteries last for several hundred cycles or more. However, the very fact that researchers have overcome both safety and voltage issues is still significant. While this won't guarantee that your devices will be completely immune to battery woes, it could be just a matter of time before you panic a little less when you drop your phone.