In Britain you employ them, in America you hide them, and in Australia and New Zealand you show them off.
A British skivvy is someone who works very hard doing dirty housework (the dictionary says usually female. Ha! As if that needed saying).
The skivvy was usually the most junior of the indoor servants. Thankfully the need for a paid post of skivvy hasn't existed since the invention of the washing machine, the vacuum cleaner, and, especially, central heating.
When skivvying is still needed nowadays it's usually done, unpaid, by the chief female of the household. This is because she is the only person in the family with the mental capabilities necessary for the perception of filth.
In America a skivvy is a man's T-shirt, but in the USA if you have skivvies then they're probably a set of men's underwear.
Australians and New Zealanders, both men and women, flaunt their skivvies quite openly.
In this case, however, skivvies are polo-necked sweaters, so it's not quite as exciting as it might be.
Spot the Frippet: skivvy. The T-shirt meaning seems originally to have been US Navy slang; the underwear meaning started off as a trade name. The origin of the name for a servant is a mystery.
For derivation-lovers I'm afraid can only really offer you skivie, which means bonkers and comes from the Old Norse skeifr, askew.