The title is Australian slang for travelling by foot with one's goods in a "Matilda" (bag) slung over one's back. The song narrates the story of an itinerant worker, or "swagman", making a drink of tea at a bush camp and capturing a sheep to eat. When the sheep's owner arrives with three police officers to arrest the worker for the theft, the worker commits suicide by drowning himself in the nearby watering hole and then goes on to haunt the site.
The original lyrics were written in 1895 by poet and nationalist Banjo Paterson. It was first published as sheet music in 1903. Extensive folklore surrounds the song and the process of its creation, to the extent that the song has its own museum, the Waltzing Matilda Centre in Winton, Queensland.
The song was first recorded in 1926 as performed by John Collinson and Russell Callow. This recording of "Waltzing Matilda" was added to the National Film and Sound Archive's Sounds of Australia Registry in 2008.
In the past I have also done Clancy of the Overflow