Rule of Thumb
The phrase is almost certainly an allusion to the fact that the first joint an adult thumb
measures roughly one inch, literally a rule (or ruler) of thumb. Since human dimensions
vary, any measurement so taken would be only a rough approximation and not to be trusted where precision was required.
The most commonly connected tale with this story is that the original rule of thumb
appeared in English Common Law. The law said that a man could not beat his wife with a
stick that was thicker than his thumb. Beating her with smaller sticks was permitted, and in some regions encouraged, to keep the woman in her place.
While it was certainly true that in many places in the past (and unfortunately to this present day), men were permitted to beat their wives, but this so-called rule was never codified. In fact, this explanation does not appear until relatively recently and its appearances are in American courts that claim such an old English law exists without citing it specifically.
Blackstone in Commentaries on the Laws of England (1765) writes, "the husband also (by the old law) might give his wife moderate correction. [...] But this power of correction was confined within reasonable bounds; and the husband was prohibited to use any violence to his wife, aliter quam ad virum, ex causa regiminis et castigationis uxoris suae, licited et rationabiliter pertinet (other than what is reasonably necessary to the discipline and correction of the wife). The civil law gave the husband the same, or a larger, authority over his wife; allowing him, for some misdemeanors, flagellis et fustibus acriter verbare uxorem
(to wound his wife severely with whips and fists); for others, only modicam castigationem adhibere (to apply modest corrective punishment)." No mention of thumbs at all.