What was done
The authors developed a well-dated high-resolution history of the atmosphere's CO2 concentration spanning the period AD 800-2000, based on measurements of stomatal density made on Tsuga heterophylla needles recovered from a sediment core that was extracted from Jay Bath (a shallow pond on Mt. Rainer, Washington, USA), after which they compared the new CO2 history with "selected temperature records."

What was learned
The three-point moving average used by Kouwenberg et al. to emphasize centennial-scale CO2 trends reveals three major peaks: one centered on approximately AD 1000, one centered in the early 1300s, and one at the end of the record in the latter half of the 20th century.  Interestingly, these are also the approximate locations of the three main peaks in the global temperature reconstruction of Mann and Jones (2003).

What it means
The authors say their results "corroborate the notion of a continuous coupling of the preindustrial atmospheric CO2 regime and climate," which posits that the air's CO2 concentration and temperature rose and fell close to simultaneously over this period.  This conclusion, however, may be challenged by the very same data that were used to obtain it; for whereas the primary trend of the Mann and Jones temperature data over the first 1100 years of their 1200-year record was decidedly downward, the concomitant primary trend of the new CO2 data was upward.  Clearly, more data will be required to resolve this major dichotomy.

Reference
Mann, M.E. and Jones, P.D.  2003.  Global surface temperatures over the past two millennia.  Geophysical Research Letters 30: 10.1029/2003GL017814.