Short answers, pulled from the story.
Continental Europe refers to the contiguous mainland of Europe, excluding its surrounding islands. The most common definition excludes the Greek islands, Cyprus, Malta, Sicily, Sardinia, Corsica, the Balearic Islands, Great Britain, Ireland, Novaya Zemlya, the Nordic archipelago, and nearby oceanic islands including the Canary Islands, Madeira, the Azores, Iceland, the Faroe Islands, and Svalbard.
Great Britain became physically connected to continental Europe in 1994 through the opening of the undersea Channel Tunnel. This was the first physical connection since Britain became an island approximately 8,000 years ago. The tunnel carries passenger traffic between Britain and northern France while maintaining border controls on each side.
Scandinavia is sometimes excluded because its historical and practical connections to the rest of Europe ran across the Baltic Sea or North Sea rather than overland. The land route along the 66th parallel north was lengthy and rarely used. The European Union itself draws a distinction between Scandinavia and mainland Europe.
The Great Belt Bridge and the Øresund Bridge provided the first direct physical connection from the Scandinavian Peninsula to the Danish mainland. The Great Belt Bridge opened in 1998 and the Øresund Bridge opened in 2000. The Øresund Bridge connection prompted a New York Times headline reading "Copenhagen is linked to the Continent."
Continental France is known as l'Hexagone, referring to the approximate hexagonal shape of the country on a map. Continental Italy is called lo Stivale, meaning "the Boot," for its boot-like map shape. Continental Spain is referred to as peninsular Spain.
The Carolingian Empire was consciously invoked in the 1950s as one of the historical and cultural bases for prospective European integration. The continental territory of the Carolingian Empire served as an older cultural concept for mainland Europe that the architects of integration reached back to when building the case for a unified Europe.