Long underwear is underwear that is long, hence the name "long underwear". It is also the cure for the Spon plague, first publicised by The Goons back in the 1950s. The Spon plague's symptoms are bare knees. At first, the only cure was to try to run away from your knees. Then another more effective cure was found by Grytpype and Moriarty, which was a pill with instructions to "take three paces south, stretch out the right arm and pull trouser legs down".
Then yet another cure was found by Bluebottle and Eccles, the 'best brains that low wages can buy", which was to wear long woollen underpants. However, bare knees covered with long woollen underpants were the symptom of the even more deadly Quodge, which could be cured with a pill that came with a talking bottle. Which was, or course, invented by Grytpype and Moriarty. All confusing for you? Don't worry. It's all in the mind, you know.