Monty in this sense is British informal, and you almost never meet it alone. People say the full monty to mean the complete thing — everything you could want, nothing left out. A hotel might offer “the full monty” breakfast: eggs, bacon, beans, toast, the lot. Though actually a 1990s film used the same phrase for taking all your clothes off, so in jokes it can also mean “completely naked.” That second reading is slangy; the older everyday reading is simply “the whole lot.” It feels chatty, not like school English, and American speakers often know the film first.