Here's the http://dx.doi.org/10.1038/nature09603 to the actual study, published in the journal Nature.
The claim of reversing aging is not really correct. The researchers created mice where they could turn the activity of an enzyme, telomerase, on or off. Telomerase is an enzyme that is important in maintaining the ends of chromosomes (called telomeres), which gradually erode as the cell divides. Mice that lack telomerase activity have eroded telomeres and show certain symptoms, such as damage to their internal organs, shrinking of brain tissue, and loss of vigor, that seem to match some of the symptoms of aging. The question is, are these symptoms of eroded telomeres permanent or will restoring the telomeres to their normal length reverse these symptoms?
To answer this question the used their mice that contained the on/off switch to control telomerase activity. They switched telomerase off to generate mice showing symptoms of telomere erosion. When they switched telomerase on again, these symptoms disappeared. Thus, this study shows that the symptoms of telomere erosion can be reversed by the activity of the telomerase enzyme (a result that is not so surprising, but useful to prove experimentally).
What significance does this have to aging in humans? It's not clear how much telomere erosion contributes to aging in humans. If telomere erosion is a major cause of aging in humans, then this work could potentially lead to therapies to reverse aging in humans (however, the techniques they use to reactivate telomerase would not work in humans, so we'd need to find new ways to increase telomerase activity in humans). However, if telomere erosion is not a major cause of aging in humans, this work may not provide such a good "cure" for aging. Although I'm not an expert in the area, I don't think that telomere erosion is the most important factor in aging, though it may play some small role. Likely, if we are to come up with some therapy to reverse aging, telomerase reactivation would be one small part of a multi-faceted approach that targets many different causes of aging.