In particular I am interested in whether it is more closely related to "precision" or "accuracy". So a somewhat mathematical description might be appropriate.
Warning - a certain amount of personal interpretation here.
When I asked Google, the definition included both "accuracy" and "precision":
I would say that it has to first be accuracy and next precision. Here is my reasoning:
You can have a very precise measurement (when you repeat it 100 times, you get the same answer within 0.1%) that has a large systematic error (bias) - for example, measuring a length with a ruler that has a worn end. Such a measurement is not faithful to the thing being measured - it's "low fidelity".
If you have a measurement that is accurate but has low precision, you can repeat it 100 times and you will slowly converge on the correct answer (since accuracy implies low bias).
This makes accuracy more important - and means that "fidelity" in a measurement, while really requiring a fair amount of both, should primarily be equated with accuracy.
It would be in reference to precision. This may sound pendantic, but every measurement in science has some degree of error no matter how small. These small errors are important, because if they repeat in subsequent experiments, then a pattern is realized. The reproducability of errors that make patterns reveal degrees of precision, (among other things). This is a critical distinction from the notion of accuracy, which assumes a thing is perfectly known. I would expect the use of the term 'fidelity' is in reference to precision, as accuracy is a unicorn in science.