Chances are, it refers to using the tip of the thumb as a unit of measurement, which would convenient, if inexact.
A commonly heard alternative, however, states the ‘rule of thumb’ was the creation of 18th-century English judge, Sir Francis Buller. He ruled (supposedly) that a man is legally permitted to beat his wife, provided he uses a stick no thicker than his thumb.
Buller was known for his overly harsh and prejudiced judgements, but there is no record of this repulsive ruling. At the time, men were permitted to admonish their wives in ‘moderation’, but the law was vague as to exactly how they could so and there was no mention of a ‘rule of thumb’.
Nevertheless, the theory against Buller was given credence by a 1782 cartoon by James Gillray. The illustration depicts Buller as ‘Judge Thumb’, carrying a couple of bundles of sticks, while a man chases a woman across the background wielding a rod above his head.