There are at least three main reasons why Australia was the last continent to be colonized by Europeans.
First, there is the simple fact that Australia is far away from Europe. Africa and Asia are, of course, relatively close to Europe. The Americas are not terribly close, but they are much closer than Australia. Since Australia was so very far away from Europe, it was less likely that any European ships would find it and then less likely that people would be sent out to colonize.
Second, there is the fact that Australia was not particularly near to any shipping lanes used by the Europeans. The Europeans did trade with the islands of what is now Indonesia, but those islands are between Australia and Europe so traders would not have been likely to find Australia by chance.
Finally, there is the fact that Australia did not have much, if anything, that Europeans wanted before they colonized it. In Asia, colonization started largely because of trade. Asian countries had things that Europeans wanted so the Europeans sent people out to settle and trade in those countries. This led to larger-scale colonization. Australia, by contrast, did not have anything that Europeans wanted to trade for and so there was no reason to start small settlements there.
For these reasons, Australia was the last continent to be colonized by Europeans.