National Geographic explains that Europe is considered a continent because it has historic and cultural rather than strict physical boundaries from Asia. While Asia and Europe are divided roughly by the Aegean Sea, the Dardanelles-Sea of Marmora-Bosporus, the Black Sea, the Caspian Sea and the Ural Mountains, the exact dividing line is still under dispute.
A continent is defined by being discrete or distinct from other large landmasses. By this definition, Europe and Asia should be considered one continent. However, historical and cultural boundaries between Europeans and Asians have turned one landmass into two continents.
Europe and Asia were first divided by the Greeks in the 6th century B.C. because of the Rioni River. Although this boundary has since shifted, cultural biases against the Mongols kept the two continents separate. Eventually, Europe as the continent became associated with Frankish lands, dividing it from Asia by culture, as well as history.
By the time of the Renaissance, scholars readopted the Greek's division of continents, and Europe as a continent became accepted as truth. Much of this had to do with the fact that Europe adopted Christianity, and this continent was roughly the size and shape of the Europe that the Greeks originally saw.