The largest island in the world outside continental landmasses is Greenland.
Greenland covers about 2,166,086 square kilometres, making it far larger than Madagascar, Borneo, or New Guinea. It lies between the Arctic Ocean and the North Atlantic, northeast of Canada and northwest of Iceland. More than 80% of its surface is covered by the Greenland Ice Sheet.
The usual qualification matters: Australia, Antarctica, and the Americas are larger, but they are generally classified as continents rather than islands. Greenland is therefore commonly described as the world's largest non-continental island. Its enormous area also makes it the largest constituent country or territory by area within the Kingdom of Denmark.
Greenland is an autonomous territory of Denmark, not an independent sovereign state. Its capital and largest city is Nuuk, and most of its population lives along the ice-free southwestern coast.