Carbon-14 has a very defined half-life of 5730 years; i.e. it takes 5,730 years for half of a sample of carbon-14 to radioactively decay into stable nitrogen-14. Through spectroscopic analysis of the ancient organic sample, by finding out what proportion of carbon-14 remains, we can accurately calculate how old it is.
But as you can see, carbon dating makes one huge assumption: radioactive decay rates remain constant and always have been constant. If this new finding is proven to be correct, even if the impact is small, it will throw the science community into a spin.
Interestingly, researchers at Purdue first noticed something awry when they were using radioactive samples for random number generation. Each decay event occurs randomly (hence the white noise you'd hear from a Geiger counter), so radioactive samples provide a non-biased random number generator.
However, when they compared their measurements with other scientists' work, the values of the published decay rates were not the same. In fact, after further research they found that not only were they not constant, but they'd vary with the seasons. Decay rates would slightly decrease during the summer and increase during the winter.