The First Parliament
South Australia Achieves Self Government in 1857
Self-government 
After 1857, with a new constitution and a Parliament, South Australia was self-governing.
The legislature (the law-making body) was now the elected Parliament, responsible only to the electorate of South Australia. Before, laws were made by the Governor in Council, responsible to the British Government.
The Executive (the body that carries out the day-to-day affairs of government) was now the Ministers drawn from the Parliament, and responsible to it.
There was still a Governor representing the British Crown, but he no longer had the powers to make decisions or appoint people to government.
The new Parliament and Executive now had almost all the powers previously held by the British Secretary of State for the Colonies, over who was appointed to official positions in the colony, over immigration, and customs (except for the power to nominate and recall South Australia's Governor).
The new government also had full power over raising and spending government money - through taxes, customs and other duties, fines and levies. It held this power until Federation, when some of the powers were handed over to the new Australian government.

So instead of a Governor responsible only to the British Government, South Australia from now on was governed by ministers responsible to a Parliament elected by the people.
Remaining links with Britain
The Governor's role now was to represent the Monarch in Britain, and as the official link between the South Australian and British Governments. The British Government still retained the right to veto South Australian legislation, until 1986 - the 150th anniversary of the founding of South Australia, but this power was rarely used.