In American speech, "new" often sounds like "ну", but some British people say "нью". (That's why the "hero" of the joke is a U.S. military guy -- because to many American ears, "ну" sounds exactly like "new" and "knew".)
Similarly, "do" (делать) and "dew" (роса) are pronounced as homophones (ду) by many Americans, but in the UK, "ду" means делать and "дью" means роса.
Other examples:
"duke" (герцог) -- US = дук, UK = дьюк
"tulip" (тюльпан) -- US = тулэп, UK= тьюлэп
Of course, I'm speaking in generalizations here -- thus, some British people say дук and some Americans say дьюк, etc.