My mother and I have begun watching The Princess of Spain on Starz which is about Catherine of Aragon. In the show they referred to Europe similar to as in current time as a whole but retaining the differences of country. We started wondering where this habit of the term Europe began. Was it after the discovery of the New World as a way to differentiate themselves? Was it during the occurrence of the events of WWI? Simply and genuinely curious .
The term Europe has a history that goes back a lot further than the discovery of the Americas or World War I. Surviving fragments of Hekataios, who lived around the 5th century BCE, already make the division between Europe and Asia, but without Africa as a separate continent. So since about 2500 years ago the Greeks have used the name Europe for generally the same area we do now (the landmass north of the Mediterranean and west of the Aegean Sea). Throughout the ancient and medieval periods, the world was often divided in three continents: Europe to the west, Asia to the east and Africa in the south. Exactly where the borders were located could be vague and changed over time.
In Greek mythology Europa was the name of a Phoenician princess who was kidnapped by Zeus and taken to Crete (so she was taken from the coasts of Asia to an island that was part of Europe). I've heard about other etymological theories involving Proto-Indo-European or Semitic words for morning or rising sun (Asia in the east) and evening or setting sun (Europe in the west), but from what I remember these origins are controversial, so hopefully someone more knowledgeable will chime in.
Sources:
Roller, D.W. (2015). Ancient Geography. The Discovery of the World in Classical Greece and Rome.
Roman L. & Roman M. (2010). Encyclopedia of Greek and Roman Mythology.