The diagram has two parts: a donut chart showing the proportion of citations per country for 1999-2003 and one for 2004-2008. The (not terribly surprising) story (or at least the interpretation of the numbers by the Royal Society) is that research has become more global. For example, in the later time period China (and Spain) superseded Australia and Switzerland (USA and Great Britain are still clearly leading the pack) in the top ten group.
I think in this case the Economist did good to refrain from using a map to display the statistics (for example, different sizes of countries do not perfectly correlate with the numbers of researchers or inhabitants and can thus lead to wrong conclusions). However, unfortunately the chart doesn’t convey much of the information contained in the text clearly. The two donut charts are mirrored, presumably to avoid clutter/tangling of the labels and and lines connecting them to the segments of the donuts. I think a line chart could have worked better. With the mirrored donuts the chart has to include all the numbers in the chart (beneath the label) in order to allow judgment of increase or decrease in all cases. With a line chart the “winners” and “loosers” would be readily apparent from the gradient of the lines.
A last fact: Interestingly, in total, citations grew by 55%, while the total number of published papers increased “only” by 33%. Does this mean scientific publications are getting more networked, citing other publications more often?
Also: Swiss researchers, explain yourselves! ;)