She was formerly a member of the New South Wales Legislative Assembly (MLA) for the district of Canterbury from 2003 to 2016 and previously a teacher.

Burney was a member of the New South Wales Legislative Assembly representing Canterbury for Labor from 2003 to 2016.

She later became the first known woman to identify as Aboriginal in the Australian House of Representatives upon her entry into federal politics at the 2016 election.

Burney was born on 25 April 1957 in Whitton,[3] a small town in south-west New South Wales near Leeton, and grew up there.

[4] She said in her inaugural speech to NSW Parliament that she did not grow up knowing her Aboriginal family, and only met her father, Nonny Ingram, in 1984.

She was raised by her elderly aunt and uncle, siblings Nina and Billy Laing, who "gave [her] the ground on which [she] stood" and taught her "the values of honesty, loyalty and respect".

[6] She was one of the first Aboriginal students to graduate from the Mitchell College of Advanced Education (now known as Charles Sturt University),[7] where she obtained a Diploma of Teaching in 1978.

[11] When Burney was elected as the Member for Canterbury in 2003, she became the first Aboriginal person to serve in the NSW Parliament.

[14] She was the lead minister in a whole of government reform plan, "Keep Them Safe", that commenced implementing the recommendations of the inquiry.

[19] She submitted her resignation to the Speaker of the NSW Legislative Assembly on 6 May 2016, and was succeeded as the state member for Canterbury by Sophie Cotsis following a by-election held on 12 November 2016.

[29] In 1996, she delivered the Frank Archibald Memorial Lecture at the University of New England, on the topic of "Education and Social Justice".

[30] As part of the 2012 Sydney Festival, Burney performed as herself delivering her inaugural speech to the NSW Parliament in a theatrical production called I am Eora.

[31] She gave the Lowitja O'Donoghue Oration at the Don Dunstan Foundation in Adelaide on 31 May 2022, in which she spoke about the Albanese government's commitment to the Uluru Statement from the Heart.