The distinction dates to 6th century BCE ancient Greece. It was derived from the idea that the important distinction was between the two sides of the Aegean Sea -- though the names 'Asia' and 'Europe' originally referred to smaller regions in western Anatolia and Greece, respectively.

I wrote an answer with several follow-ups here last year, which also cites another previous answer that I wrote that has more details about the origins of the names. Give a yell if there's anything you want to follow up on!