What was done
The authors review an immense wealth of evidence pertaining to the climatic and environmental history of the earth over the last millennium, although stating that "the adopted period of 1000 years is strictly a convenience that merits little scientific weight."  Indeed, the important study of Esper et al. (2002) suggests that the peak warmth of the Medieval Warm Period actually occurred just prior to the past millennium at approximately the year 990.

What was learned
In the words of the authors, "the assemblage of local representations of climate establishes both the Little Ice Age and Medieval Warm Period as climatic anomalies with worldwide imprints, extending earlier results by Bryson et al. (1963), Lamb (1965), and numerous intervening research efforts."  In addition, they find that "across the world, many records reveal that the 20th century is probably not the warmest nor a uniquely extreme climatic period of the last millennium."

What it means
Contrary to the data-poor claims of climate alarmists, the 20th century temperature rise that ushered in the Modern Warm Period did not produce a climate that is warmer than that of the Medieval Warm Period.  Also, since the atmospheric CO2 concentration of that earlier warm period was much lower than that of the present warm period, there is no reason why the warmth of the present should be attributed to the CO2 increase that has occurred in the interim.

References
Bryson, R.A., Arakawa, H., Aschmann, H.H. and Baerris, D.A. plus 36 others.  1963.  NCAR Technical Note. In: Bryson R.A., and Julian P.R. (Eds.) Proceedings of the Conference on Climate of the 11th and 16th Centuries, Aspen CO, June 16-24 1962, National Center for Atmospheric Research Technical Notes 63-1, Boulder, CO.

Esper, J., Cook, E.R. and Schweingruber, F.H.  2002.  Low-frequency signals in long tree-ring chronologies for reconstructing past temperature variability.  Science 295: 2250-2253.

Lamb, H.H.  1965.  The early medieval warm epoch and its sequel.  Palaeogeography, Palaeoclimatology, Palaeoecology 1: 13-37.