The Greenland ice sheet covers 80% of the island with a thickness of generally more than 2 km. If the entire ice cap melted it would cause a global rise in sea levels of 7.2 metres, dramatically affecting coastal regions around the world, but what would the island of Greenland itself look like ? Wikipedia has the answers.
As this image (based on the ETOPO1 Global Relief Model) shows, much of the bedrock is actually at or below sea level. This is due to the weight of ice depressing the central areas of Greenland.
If the Ice melted Greenland would most likely initially appear as an archipelago. Over the course of thousands of years, the surface would rebound (isostasy), and probably rise above sea level again.