The colloquial Australian-English noun budgie smuggler(s) denotes a pair of short, tight-fitting men’s swimming trunks.

This noun refers to the appearance of the male genitals in figure-hugging trunks—budgie being a colloquial abbreviation of budgerigar, denoting a small Australian parrot. This was explained by Reg Henry in One vote for Olympian modesty, published in the Pittsburgh Post-Gazette (Pittsburgh, Pennsylvania) of Wednesday 13^th August 2008—Reg Henry recalls “the Speedos of [his] youth”:

The Speedo company was founded in Australia and many is the summer I put on one of their suits—you didn’t get much material for your money—in order to impress the girls.
[…]
Back then […], a Speedo suit was shockingly revealing considering the strait-laced times. While it was thought (by men) to turn every fellow into Greek statuary with a fig leaf of nylon covering, it mostly revealed male vanity and absurdness.
Indeed, so vulgar and gross were these male mating displays on public beaches that the Aussies came up with an expression for the abbreviated Speedo—the budgie smuggler. Budgie is short for budgerigar, the native Australian parakeet, and the idea was that a fine figure of a man would wow the crowd if he looked like he had a parrot up his pants.

The noun budgie smugglers is first recorded in Past Sports Stars and Gender, the fifth episode, broadcast on Monday 14^th September 1998, of the first season of the Australian television series The Games *—John, played by John Clarke, says the following to Bryan, played by Bryan Dawe:

Des Renford would regularly take on the English Channel, Bryan. He would drop his tweeds, pull on a pair of oversized budgie smugglers, and he would drop a bomb off the white cliffs of Dover and start rolling his arm over.

* The Games was an Australian mockumentary television series about the 2000 Summer Olympics in Sydney. The first season was broadcast in 1998, the second in 2000, on the Australian Broadcasting Corporation. Written by John Clarke (1948-2017) and Ross Stevenson (Ross Campbell – born 1957), this television series starred John Clarke and Bryan Dawe (born 1948).

According to Matthew Brace in Yanks blamed as Aussies lose their biscuit, published in The Times (London, England) of Saturday 17^th January 2004, the noun budgie smugglers was already going out of use:

Australians are lamenting the erosion of their vernacular. Or, to put it another way: “Strewth Bruce, the old Strine’s goin’ down the gurgler”.
Some language experts believe that classic phrases are vanishing. “Sheilas” are becoming “chics” and “babes”, and “fair dinkum” is being replaced with the bland “absolutely” or “honest”.
Racing commentators no longer scream into the microphone that the nags were out of the gates and “off like a bride’s nightie”, but that they ran rather fast. Nor do they accuse the jockey who missed a fence of having “kangaroos in his top paddock”, but that he was, simply, a bit mad.
Other rich phrases in the Australian vernacular now rarely heard include “to pass in your marbles”, meaning to die, “budgie smugglers”, referring to tight swimming trunks, “date”, or backside, “grouse”, for great, and “Hell, West and Crooked”, which Queenslanders use to mean an utter disaster.

The Australian linguist Kathryn Burridge mentioned the noun budgie smugglers in Where do body parts come from?, in Weeds in the Garden of Words: Further observations on the tangled history of the English language (Cambridge University Press, 2005):

Whether we’re producing names for new concepts or simply adding to the names of old ones, metaphor is often behind it all. We are always adapting familiar structures from our experiences to new purposes and our body part terminology supplies wonderful illustrations of this. Many of the figures we create are very inventive and there’s a lot of verbal play involved. I think my favourite example is still the miraculous pitcher, that holds water with the mouth downwards. This extraordinary example comes from the 18^th century—it was a euphemism for ‘vagina’. (But then again, Australian English budgie smugglers for a ‘tight pair of men’s swimming trunks’ would come a close second!)

Caricature of Tony Abbott, sold as a dog toy (2013)—photograph: Museums Victoria:
—Anthony Abbott (born 1957), member of the Australian Liberal Party, was Leader of the Opposition from December 2009 to 2013. Well known for his physical prowess and sportsmanship, particularly his participation in triathlons, Abbott was regularly lampooned for wearing budgie smugglers: