Something insignificant, not worth even a moment’s consideration. Example: ‘he doesn’t give a tinker’s damn about what happens.’
The OED defines ‘tinker’ as “a craftsman (usually itinerant) who mends pots, kettles, and other metal household utensils.” Back in the 1700s and 1800s, tinkers were pretty much at the bottom of the social scale, along with vagrants and Gypsies, and they had a well-known tendency to include a swearword in every sentence. Expressions such as ‘to swear like a tinker,’ ‘a tinker’s curse or damn,’ and ‘as drunk or as quarrelsome as a tinker,’ were common.
Expressions like ‘not give a curse/damn’ or ‘not worth a curse/damn’ were also often used. In 1760, Oliver Goldsmith wrote in an essay: “Not that I care three damns what figure I may cut.”
‘Tinker’s damn’ has been in print since 1839, when Henry David Thoreau wrote in his journal, “’Tis true they are not worth a tinker’s damn. ”
In the Grant County Herald, Wisconsin, 1854, we have: “There never was a book gotten up by authority and State pay, that was worth a tinker’s cuss.”
In the Practical Dictionary of Mechanics of 1877, Edward Knight gives this definition, (note the difference in spelling): “Tinker’s-dam: a wall of dough raised around a place which a plumber desires to flood with a coat of solder. The material can be but once used; being consequently thrown away as worthless.”
The OED calls Knight’s suggestion “an ingenious but baseless conjecture.” Most sources seem to think it’s not worth a tinker’s damn. It would appear that the spelling of the phrase as ‘tinker’s dam’ came about to soothe the sensibilities of those who did not wish to use even such a mild oath as ‘damn.’
Others wish to find something of mystery and interest in the most ordinary of expressions, and have a tendency to believe that if an ingenious story seems to neatly fit the bill then it must be true. Humans are very good at ingenious explanations, but often they’re simply not true, as in this case.
Tinkers used swearwords so much that they came to have no meaning to those who heard them, and perhaps not to the tinkers themselves. We do the same thing today, with words and phrases that are fads, or used so much that we don’t even hear them anymore. For example, ‘have a nice day!’
So, go ahead, have one!