We get this headline every six months or so. The experiment is cool, and drives down the precision to new levels, but I’ll give the standard disclaimer: it’s a frequency standard, not a clock.
The logic clock is based on a single aluminum ion (electrically charged atom) trapped by electric fields and vibrating at ultraviolet light frequencies, which are 100,000 times higher than microwave frequencies used in NIST-F1 and other similar time standards around the world. Optical clocks thus divide time into smaller units, and could someday lead to time standards more than 100 times as accurate as today’s microwave standards. Higher frequency is one of a variety of factors that enables improved precision and accuracy.
Update: an article from Wired which has the virtue of calling it a frequency standard. Unfortunately, it sort of implies that we haven’t already measured gravitational time dilation, which of course we have, and (as I mentioned previously) has even been measured by amateur time nuts.