The Statute of Westminster was the enactment of the United Kingdom Parliament (December 11, 1931) by which that body renounced legislative authority in the self-governing overseas Dominions of the British Empire, formalizing the independence of Canada, Australia, New Zealand, South Africa and Newfoundland, except in relation to revision of constitutions founded in British legislation. Further, the Statute did not apply to Australia, New Zealand or Newfoundland unless and until adopted by those Dominions' Parliaments. Adoption of the Statute was strongly opposed by conservatives in Australia, and it was not until 1942 that it was finally adopted to clarify Government war powers (the adoption was backdated to the start of WWII in September 1939). New Zealand adopted the Statute in 1947. Newfoundland never adopted the Statute - Britain resumed direct rule in the 30s and retained it until Newfoundland became a Province of Canada in 1949.
The key passage of the Statute provides that "No Act of Parliament of the United Kingdom passed after the commencement of this Act shall extend or be deemed to extend, to a Dominion as part of the law of that Dominion, unless it is expressly declared in that Act that that Dominion has requested, and consented to, the enactment thereof."
It was also enacted that "No law and no provision of any law made after the commencement of this Act by the Parliament of a Dominion shall be void or inoperative on the ground that it is repugnant to the law of England, or to the provisions of any existing or future Act of Parliament of the United Kingdom, or to any order, rule, or regulation made under any such Act, and the powers of the Parliament of a Dominion shall include the power to repeal or amend any such Act, order, rule or regulation in so far as the same is part of the law of the Dominion."
Despite the provisions of the Statute of Westminster, the British Parliament still had the power to pass legislation regarding the Canadian constitution and the Australian states. These powers were removed by the Canada Act 1982 and the Australia Act 1986.