I was sure that it had something to do with the distance that could be ridden by horses, but according to our friend Wikipedia, it comes from an Old English word (*þriding ) which descends from an Old Norse word (þrithjungr) for ⅓ of [a county].
Source: https://en.wikipedia.org/wiki/Riding_(country_subdivision)
Thanks for asking this. I thought to look it up a couple of times today to satisfy my own curiosity, but didn’t quite get there.