The Australian Flag was chosen in 1901 after a worldwide design competition was held following Federation. On the 3rd of September 1901 the new flag flew for the first time on top of the Royal Exhibition Building in Melbourne.
Before 1901, Australia was a collection of six British colonies and each colony had its own flag based on the Union Flag of the British Empire.
The Flag uses three important symbols, the Union Jack, the Commonwealth Star and the Southern Cross.
The Union Jack in the upper hoist quarter symbolises Australian history as six British colonies and the principles upon which the Australian Federation is based and demonstrates loyalty to the British Empire.
The Commonwealth Star in the lower hoist quarter represents the six colonies and the Australian Territories. Originally the Commonwealth Star had six points, which represented the six colonies, but this was changed in 1908 when a seventh point was added to symbolise the Territory of Papua and any future territories.
The Southern Cross constellation of five white stars, one small five pointed star and four larger seven pointed stars has been used to represent Australia since the early days of British settlement and is one of the most distinctive constellations visible in the Southern Hemisphere.
There are a number of other Flags of Australia including the Australian Aboriginal Flag, The Torres Strait Islander Flag and the Flags of the Australian Defence Forces.
You may also want to have a look at the list of Australian Flags at Wikipedia