The model you see here doesn't predict the future--but it does illustrate one possible outcome of polar ice sheet meltdown. It shows the southern end of Manhattan Island, a borough currently home to more than 1.5 million people, under 3 and 5 meters (about 10 and 16 feet) of sea-level rise. The higher amount would occur if a significant part of the ice sheets in Greenland or Antarctica melted--a scenario experts consider unlikely to happen anytime soon.
Is this how Manhattan would really look, centuries to thousands of years in the future, as sea levels got higher? Probably not, because we would, at enormous expense, build sea walls and pumps to protect the city's complex infrastructure.