This is a question that has both a literal and symbolic answer. On the literal side, one can argue from the enotes reference link:
Comprising the westernmost peninsula of Eurasia, Europe is generally divided from Asia to its east by the water divide of the Ural Mountains, the Ural River, the Caspian Sea, the Caucasus Mountains (or the Kuma-Manych Depression), and the Black Sea to the southeast. Europe is bordered by the Arctic Ocean and other bodies of water to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south, and the Black Sea and connected waterways to the southeast.
This can help to give some background as to the dimensions of Europe. However, the very next sentence in the article argues the very symbolic nature of the question that makes it dificult to fully answer: "Yet the borders for Europe—a concept dating back to classical antiquity—are somewhat arbitrary, as the term continent can refer to a cultural and political distinction or a physiographic one." With a globalized world setting, I think that the borders of all nations and continents are disappearing. Information technology and communication advances are making the distinct and set boundaries more fluid and mobile. The reality is that it is difficult to define where Europe ends and where it begins as the world becomes more interconnected and globally dependent. Add this to the historical dimension with Europe being the center of exploration and the first world power to establish the globalized world through its exploration, and one finds it more difficult to establish where Europe ends and where it begins.
This is either a very simple question or a very difficult question -- depending on if we are talking about physical or cultural borders.
Physically, there is no reason to call Europe a separate continent (separate from Asia). However, there is a commonly accepted definition of Europe that says it is separated from Asia by
Culturally, it is much harder to define where Europe ends. This is especially true in modern times when the influence of Europe has spread so far and European peoples have colonized the Americas and Australia and New Zealand. There was a time when Europe was defined as pretty much the same thing as Christendom, but Christendom and Europe are no longer geographically the same thing (or anywhere near it).
I do think that most people would still define Europe (culturally) as the lands that have been Christian since before the Renaissance. This means that Europe would include Russia and Romania but also Iceland and England. This is not a perfect definition, but I think that it captures how most people think about Europe.