Geologically, Iceland is part of the Mid-Atlantic ridge and sits on two tectonic plates with America to the west and Europe to the east, making it part of both the North American and European continents. Politically, however, Iceland is part of Europe.
Iceland is Europe's most westerly country, but its location to the west of mainland Europe means that it doesn't lie solely on the European tectonic plate. In fact, Iceland lies at a point where the European and American tectonic plates are slowly diverging. Due to this position on both the American and the European tectonic plates, it can be argued that Iceland lies on the continents of both Europe and North America.