Australia was once part of the commonwealth or the British empire, which is reflected in the flag.
Hawaii
Hawaii
The British flag is in the Canadian Coat of Arms because the Canada was formed from British colonies.
The Australian flag has the union flag in the top left because Australia used to be part of the British empire. There are actually many flags with the union flag in the top left. Any place that was part of the British empire when it developed its flag will have the union flag in the top left.
Because of Hawaii's relationship with the British. The Hawaiian king originally flew the British Union flag on its own, but a group of advisor's recommended it be changed to include stripes to represent the islands he had united.
Australia was once a British colony, and so holds the Union Flag within it's flag to represent this. This is the same for all flags which hold the Union Flag as part of their flag. Almost all (with the exception of a small few) countries that were/are part of the Commonwealth were British colonies, and therefore may hold the Union Flag within their own flag.
The Red Ensign is the national flag flown on British non-military boats and ships. The White Ensign is flown on military vessels.
Because New Zealand used to be a British colony, it is also part of the Commonwealth of Nations.
The Beatles
Australia was a British colony, and adapted their flag from the British flag.
The union jack on the Australian Flag is from the first white people to settle on our land, the British. The British flag is JUST the union jack, so, to celebrate the people who first settled in Australia, we have their flag in part of OUR flag. Hope that helps :)