The area 'down under' your pants, generally referring to your genitals.
1) We're going to a party? Alright, but I gotta head home and shower first. My Australian parts need a little air.
variation:
2) - Did you buy that girl a drink?
- Yeah, she's Australian.
- Oh, so that's why she sounds funny.
- Yeah, and if things go well I'll get to tour down under and frollick in the outback.
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