By definition, heart rate variability is the time between each heart beat. This is called the R-R interval and shows the beat modulation of the sino-atrial node whose time variation is controlled by the autonomic nervous system. This matters because sympathetic (fight or flight) or parasympathetic (rest and digest) activity governs cardiac dynamics. A higher HRV is generally taken as a marker of healthy autonomic nervous system.
How is it measured: It is measured by smart watches or by ECG in a quiet supine position. It is analyzed in the time dimension by standard methods of variation:Standard deviation, Root mean square, and a percentage change above a certain value. It can also be measured by spectral analysis of R-R series to high-med-low frequencies. These frequency changes can be dependent on related phenomenon. For example vagus/parasympathetic affects the high frequency changes, the slower is affected by baroflex, hormones.
Its acceptance came about after the Task force report from the European society of Cardiology and American Society of Pacing and Electrophysiology. There is significant evidence of its importance for cardiovascular events and all cause mortality (https://pmc.ncbi.nlm.nih.gov/articles/PMC12047215/) and for hypertension (https://pubmed.ncbi.nlm.nih.gov/9719057/) (https://pmc.ncbi.nlm.nih.gov/articles/PMC12497352/).
If HRV reflects the sympathetic and parasympathetic tone, then practices such as meditation may affect it and there is literature that it is not significant (meta analysis: https://pmc.ncbi.nlm.nih.gov/articles/PMC8243562/) to significant (https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0243488). This might be affected by the link between blood pressure and meditation (https://www.sciencedirect.com/science/article/pii/S0965229924000724?via%3Dihub) though majority of the hypertension studies did not report the effect size.