Heart Rate Variability is one of those things that has such an obvious meaning I feel dumb asking follow up questions, but is consistently used in ways that confuse me. It sounds a lot like arrhythmia, which is bad, but The Willpower Instinct consistently refers to it as good. Plus it refers to it changing in ways that must be measured instantaneously, but changes in variability have to be measured over time, right?
Here is what I have figured out: we (I) think of the heart as beating to A Rhythm, which is your BPM. The rhythm can speed up or slow down, but it’s still a rhythm. A deviation from that is an arrhythmia, which is Bad. We (I) think this because the wikipedia article on sinus rhythm basically says it, and because the article on HRV implies it’s measured in five minute increments over 24 hours, which means it’s basically a measure of range. But at least some of the time HRV refers to beat-to-beat variation, and it’s being measured in response to an immediate stimulus (although, maddeningly, no one specifies the time period).
Your parasympathetic (relaxed/restorative) nervous system sends signals to your heart to decrease your heart rate. Your sympathetic (fight/flight/freeze) system sends signals to increase it. High parasympathetic activity also seems to be associated with high variability, at least to a point. My personal guess is that high variability indicates both systems are operating and interacting, while low variability indicates one has taken over, and that your body is somewhat biased towards a higher rate, so it takes a bigger push from the parasympathetic to get the rate down. Having one system dominate is not always bad: when you are running from a tiger, your heart should beat as fast as possible and redirect blood from digestion and immune system to muscles. And when you are truly safe, the parasympathetic tells your body it can safely pay off it’s technical debt. But often having both, and being able to switch between the two, is useful.
There’s a lot of data showing high heart rate variability is increased by known Good Things (meditation, exercise), and low HRV is associated with bad things (alcoholism, PTSD), but I don’t see hard enough data on causality that I’m confident of the direction.
Aceso Under Glass 
My understanding is that the sympathetic and parasympathetic nervous systems affect heart rate variability with different frequency profiles, so if you do a discrete Fourier transform on the heart rate variability it becomes easier to see how activated one or the other is.
The bottom left picture is a Power Spectral Density graph (graph of how much variability is at different frequencies) and shows what I’m talking about.
I don’t understand which is sympathetic and which is parasympathetic