The clocks operate using an “optical lattice” of lasers, which trap atoms of ytterbium and monitor them as they switch between two energy states, which acts as the “ticking” of the clock. According to the text of the study: “By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity…However, the theory of relativity prescribes that the passage of time is not absolute, but is affected by an observer’s reference frame.”
Remember all that stuff people told you in school about how a planet’s mass warps space and time like a weight on rubber sheet? That’s happening right now, though we don’t notice it. These ytterbium optical lattice clocks do, however. If you move one farther away from the surface of the Earth, its time-keeping will reflect the decreased effect of gravity. This extreme sensitivity means that they could be used to figure out the shape of the Earth with an error margin of around 1 centimeter, based on a branch of mathematics called geodesy.
In addition to accurate measuring the Earth and the passage of time, these clocks might also be used to detect gravitational waves or even dark matter, provided that the latter acts the way we think it does. Unfortunately for hardcore timekeeping enthusiasts, however, there are no plans to make these clocks available to the public.