LED lights are more efficient than CFLs (and far more efficient than incandescent lightbulbs) for one simple reason: LEDs don’t generate heat as part of the illumination process.
LEDs don’t have a filament, so not only can they not burn out, but they don’t waste any energy when producing light. In an incandescent bulb, electric current runs through the filament, heating it up until it glows and produces light. All of the heat produced is a complete waste of energy, as the point of incandescents is illumination, not heat production.
In CFLs, electric current passes through a tube filled with argon and mercury vapor. That generates ultraviolet light, which in turn strikes and excites a a fluorescent coating on the inside of the tube, which in turn produces the visible light you see when you turn a compact fluorescent bulb on.
LEDs produce light via the movement of electrons in a semiconductor material, so it’s an entirely different process. Almost no energy is wasted in light producing LEDs, with nearly all the electric current going toward the production of light.