What was done
The authors used an eight-year time series (1993-2001) of Arctic sea-ice thickness derived from measurements of ice freeboard made by 13.8-GHz radar altimeters carried aboard ERS-1 and 2 satellites to determine the mean thickness and variability of Arctic sea ice between latitudes 65 and 81.5°N, which region covers the entire circumference of the Arctic Ocean, including the Beaufort, Chukchi, East Siberian, Kara, Laptev, Barents and Greenland Seas.

What was learned (1)
Mean winter sea-ice thickness over the region of coverage was found to be 2.73 meters with a standard deviation of ± 9% of the average, which variability was 50% greater than that predicted by climate models, "and probably more," say the authors, as they report that their analysis "excludes variability that occurs over timescales of longer than a decade."

What it means (1)
Their authors specifically note that their observations "show an interannual variability in ice thickness at higher frequency, and of greater amplitude, than simulated by regional Arctic models," which clearly indicates that the models do not reproduce reality very well in this regard.

What was learned (2)
The authors note that "the interannual variability in thickness [9%] compares with a variability in mean annual ice extent of 1.7% during the same period."

What it means (2)
This finding, in the words of the authors, "undermines the conclusion from numerical models that changes in ice thickness occur on much longer timescales than changes in ice extent," which indicates that the models do not reproduce reality very well in this respect either.

What was learned (3)
Investigating the origin of Arctic sea-ice thickness variability, the authors discovered "a significant (R² = 0.924) correlation between the change in the altimeter-derived thickness between consecutive winters, and the melt season length during the intervening summer."

What it means (3)
In the words of the authors, "the observed dominant control of summer melt on the interannual variability of mean ice thickness is in sharp contrast with the majority of models, which suggest that ice thickness variability in the Arctic Ocean is controlled mainly by wind and ocean forcing."  This fact highlights yet another failure on the part of the models.

What was learned (4)
The authors' data demonstrate "that sea ice mass can change by up to 16% within one year."

What it means (4)
This finding, in the words of the authors, "contrasts with the concept of a slowly dwindling ice pack, produced by greenhouse warming," which represents still another strike against the models.  Hey, why do they get four strikes before being called out?

What it means (1-4)
The authors simply state that their results "show that errors are present in current simulations of Arctic sea ice," concluding in their closing sentence, therefore, that "until models properly reproduce the observed high-frequency, and thermodynamically driven, variability in sea ice thickness, simulations of both recent, and future, changes in Arctic ice cover will be open to question."