Explain Like I'm 5 (ELI5)

TL;DR: the ancient Greeks, with their limited knowledge of geography and abilities to travel, first employed the word "Europe" to define the boundary between their known world, the unknown to the East (Asia) and the unknown to the South (Africa).

quote from the dedicated wikipedia page:

The threefold division of the Old World into Africa, Asia, and Europe has been in use since the 6th century BC by early Greek geographers such as Anaximander and Hecataeus.

Anaximander placed the boundary between Asia and Europe along the Phasis River (the modern Rioni in Georgia in the Caucasus Mountains), from Rioni mouth in Poti on the Black Sea coast, through the Surami Pass and along the Kura River to the Caspian Sea, a convention still followed by Herodotus in the 5th century BC. As geographic knowledge of the Greeks increased during the Hellenistic period, this archaic convention was revised, and the boundary between Asia and Europe was now considered to be the Tanais (the modern Don River). This is the convention used by Roman era authors such as Posidonius, Strabo and Ptolemy.

Geologically, Europe has its own tectonic plate, which is being smashed against the Asian one at the Ural mountain range.
Culturally, geographically, historically and politically, Europe and Asia are also very different, so a separation makes sense.
But most of all, the people doing the naming and categorizing were Europeans, and of course they get their own continent.

I don't know about the rest of the world, but in Ukrainian middle schools on geography lessons we are taught that there are continents and there are "Parts of the World". Europe and Asia are two separate Parts of the World, but they are the same continent - Eurasia. North America and South America are both separate Parts of the World and continents.