Why is Australia called Australia?

The name Australia comes from the Latin term 'terra australis incognita', meaning "unknown southern land", because for so long the continent of Australia was theorised, but not realised.

Matthew Flinders did not discover Australia, but he was the first to circumnavigate the continent. He suggested the name "Terra Australis" and this became Australia, the name officially adopted in 1824. When all the colonies federated to become states under a central government in 1901, the name Commonwealth of Australia was adopted for the new nation.

Prior to this, Australia was known by the Dutch as New Holland (from the early 1600s), whilst in 1770 James Cook claimed the eastern half of the continent as New South Wales, on behalf of England.
For more details on how the term Terra Australis originally came about, please see the related link.