"Land Down Under" is a colloquial name for Australia, referencing its position in the Southern Hemisphere—"down under" the equator and the bulk of the world's landmass and population.
The phrase predates European settlement. Indigenous Australians (Aboriginal and Torres Strait Islander peoples) conceptualized their continent's relationship to the cosmos in ways that European cartographers later flattened into "Terra Australis Incognita" (Unknown Southern Land). The specific English phrasing gained currency in 19th-century British naval and emigrant writing, then exploded globally with Men at Work's 1981 hit song.
Australians use it themselves—often with irony or pride. It's informal, not official. The national anthem ("Advance Australia Fair") doesn't mention it. "Oz" and "Straya" are other common nicknames.
The phrase centers a Northern Hemisphere perspective—Australia isn't "down" to Australians. But as a global shorthand for a continent-country of ancient cultures, unique ecology, and modern multicultural society, it endures.