Wikipedia has a good summary of what it means. In the book, Hank Martin (the time traveler) tries to explain that although you might get paid twice as much as people in another region, if the prices you pay for goods are more than double, you are worse off (the audience wasn't buying it). Here is Crampton's post from 2013:
"Mark Twain channels the frustration of thousands of future Econ 104 lecturers confounded by popular unwillingness to note the difference between the nominal and the real.
Twain's Connecticut Yankee tries to explain to some local freemen that the combination of high wages and high prices in their part of the country, still protected by tariffs, makes them worse off than the combination of lower wages and lower prices in his part of the country, where they have been easing towards free trade.*
After explaining, in what he thought was a crusher, that wages were twice as high in the protected region but that prices were more than twice as high, his audience still preferred higher nominal wages.
You'd think things would be better a few centuries later..."Wait! Now, you see, the thing is very simple; this time you'll understand it. For instance, it takes your woman 42 days to earn her gown, at 2 mills a day—7 weeks' work; but ours earns hers in forty days—two days short of 7 weeks. Your woman has a gown, and her whole seven weeks wages are gone; ours has a gown, and two days' wages left, to buy something else with. There—now you understand it!"He looked—well, he merely looked dubious, it's the most I can say; so did the others. I waited—to let the thing work. Dowley spoke at last—and betrayed the fact that he actually hadn't gotten away from his rooted and grounded superstitions yet. He said, with a trifle of hesitancy:"But—but—ye cannot fail to grant that two mills a day is better than one."Shucks! Well, of course, I hated to give it up. So I chanced another flyer:"Let us suppose a case. Suppose one of your journeymen goes out and buys the following articles:"1 pound of salt; 1 dozen eggs; 1 dozen pints of beer; 1 bushel of wheat; 1 tow-linen suit; 5 pounds of beef; 5 pounds of mutton."The lot will cost him 32 cents. It takes him 32 working days to earn the money—5 weeks and 2 days. Let him come to us and work 32 days at half the wages; he can buy all those things for a shade under 14 1/2 cents; they will cost him a shade under 29 days' work, and he will have about half a week's wages over. Carry it through the year; he would save nearly a week's wages every two months, your man nothing; thus saving five or six weeks' wages in a year, your man not a cent. Now I reckon you understand that 'high wages' and 'low wages' are phrases that don't mean anything in the world until you find out which of them will buy the most!"It was a crusher.But, alas! it didn't crush. No, I had to give it up. What those people valued was high wages; it didn't seem to be a matter of any consequence to them whether the high wages would buy anything or not. They stood for "protection," and swore by it, which was reasonable enough, because interested parties had gulled them into the notion that it was protection which had created their high wages. I proved to them that in a quarter of a century their wages had advanced but 30 per cent., while the cost of living had gone up 100; and that with us, in a shorter time, wages had advanced 40 per cent. while the cost of living had gone steadily down. But it didn't do any good. Nothing could unseat their strange beliefs.Well, I was smarting under a sense of defeat. Undeserved defeat, but what of that? That didn't soften the smart any. And to think of the circumstances! the first statesman of the age, the capablest man, the best-informed man in the entire world, the loftiest uncrowned head that had moved through the clouds of any political firmament for centuries, sitting here apparently defeated in argument by an ignorant country blacksmith! And I could see that those others were sorry for me—which made me blush till I could smell my whiskers scorching.
* It would be a fun exam question to have students lay out the conditions under which Twain's stylised facts could be true. The Boss has instituted a common coinage with lots of small change, so the big problem of small change doesn't apply. He also has been, region by region, easing back tariff protections and moving towards free trade. In Region 1, free trade is almost entirely in place; in Region 2, liberalisation hasn't started. Wages across all sectors are lower in Region 1, but prices are sufficiently lower to make real wages higher. Region 2 has higher nominal wages across the board. It is illegal under feudal structures for workers to move across regions, and it's close to illegal for them to change professions (though it seems to depend on the profession). So labour markets should only in the long term through Malthusean effects: sectors with higher real wages see higher population growth while sectors with lower real wages see starvation and decline.
I can, in that set up, see large wage effects in the import-competing sector under liberalisation. But Twain also has the wages of mechanics being lower. In the high tariff region, a master bailiff, master hind, carter, shepherd and swineherd earn 50 milrays a day: twice what they earn in the low tariff region (a milray is a hundredth of a cent). In the high tariff region, mechanics, carpenters, dauber, masons, painters, blacksmiths, and wheelwrights get a full cent a day; in the low tariff region, half. A woman labouring on a farm earns two mills a day (10 milrays, a tenth of a cent) in the high tariff region and half that in the low tariff region. So what in this counts as an import-competing sector? I'd say the shepherd to the extent that the sheep's main product is traded wool rather than non-traded meat (food preservation not yet in a state to allow meat transport across regions); the blacksmith to the extent that he makes wrought iron works for sale rather than repairs to farmers' carts; and farm labour to the extent that they work on transportable wheat and grain rather than livestock.
But Twain allows no variation in the ratio of wages between the high and low tariff regions across sectors. Maybe transportation costs in all of those sectors prevent those workers' product from moving anyway, but Twain has meat being less than half the price in the free trade region (either salt meat moves or forage does); eggs at less than half the price; wheat at 4/9ths the price; clothing at 6/13th to 1/2 the price. He also has beer being cheaper in the free trade region. And it isn't like wages in the non-traded sector are bid down by exit from the traded sector - labour mobility across sectors seems pretty limited. Maybe there's an auxillary unstated assumption that the Lords in the trade experiment regions are commanding that labourers make the appropriate movements across sectors such that we get to the observed equilibrium."