So you know how you learned in high school about carbon dating be a super reliable way of measuring the age of things, since the amount of C-14 in organic material decreases at a steady rate?
The amount of (mildly) radioactive Carbon-14 in organic materials does slowly decrease. But exactly how slowly or quickly depends upon two additional factors: how much C-14 is present in the atmosphere around that sample, and how much the C-14 is also triggered to decay. And fascinatingly, it turns out that the Sun of all things influences both of those!
Specifically the Sun's neutrino output. Neutrinos are high energy but low mass particles that the Sun creates in the process of nuclear fusion. When these particles collide with Nitrogen-14 in the atmosphere, they cause the N-14 to convert to C-14. Therefore if there's more neutrinos coming out from the Sun than usual, we'll have more C-14 than usual, so C-14 will appear to decay more slowly than usual, so in order to get a large amount of decay we'd need a super-large amount of time, so (if we assumed it was decaying at the same rate as usual) we would be estimating times too short.
On the other hand, there's a competing effect too. C-14 naturally decays, however it can be stimulated to decay faster, and in fact neutrinos can do this too. So if htere's more neutrinos coming from the Sun, C-14 will be decaying faster than usual, so to get a large amount of decay we'd need only a small amount of time, so (if we assumed it was decaying at the same rate as usual) we would be estimating times too long.
Now here's what's interesting. If we compare the ages of trees based upon carbon dating to their ages based upon tree rings, we can try and calibrate the rate of C-14 decay to what's really happening. While the authors of the linked paper didn't specify which of the two effects dominated (that is, it's unclear to me if excess neutrinos would result in MORE or LESS C-14 overall, and thus over- or underestimate the ages of trees using C-14), they did say that there's a 200-year period to the "anomalies" in carbon-dating results as compared to tree rings. So if the anomalies are caused by the Sun's neutrino output, that means that the Sun's nuclear fusion (which creates the neutrinos) is varying on a 200-year cycle.
Why hello, Mr. Variable Star!