Used as a general descriptor for men's underwear regardless of whether the garment in question is a pair of briefs, boxer shorts, etc. It's important to note that one cannot "go commando" and say they have a "nut-hut"; however, the defintion could be expanded to include athletic supporters (i.e. "jockstraps")
Rather than saying "It's hot out today and my balls are rather moist," one now has the option of stating "It's so hot today there's a sweat lodge in my nut-hut." This usage is equally valid whether the speaker is wearing underwear and/or an athletic supporter.