The remark means both lack of history and lack of customs and enthicity etc, and when thought about is really a silly accusation in two ways a) modern Australia is only 200yrs old, hardly enough time to evolve anything that would resemble its own seperate culture especially when it barely has its own identity. b) Australia actually does have a wonderful history and culture, it is just not a white one so is rather arrogantly overlooked by many, including white Australians.
The "Australia has not real culture" remark is a real sore point to many Australians, for some odd reason many Australians feel they should be able to compete, historically, with Europe.