This is the Tasmanian name for the puffer jacket, in particular the jacket in black which, in Tasmania, can be worn on formal or informal occasions. This is a colloquialism born in Tasmania so it is Tasmanians taking the mickey out of themselves rather than us mainlanders poking fun at them. Tasmanians are proud of their ability to dress down with style, it would seem.
Underneath the Tassie tuxedo you may well find a flannie (a flanellette shirt) which would identify the wearer as a bogan and as someone living beyond the Flannelette Curtain, a demarcation line between Hobart and the bogan territory of Glenorchy. Other cities have similar ideas with different names. The Red Rooster line (Sydney) and the Hipster-Proof Fence (Melbourne).