It's an "autonomous territory" of Denmark. Think of it like a colony, except the Danes don't consider it as such because it would be bad PR.
Greenland has close to no cultural ties to Denmark, and Danes tend to be quite racist towards Inuits. The argument is that they're too poor to be out on their own, but we all know it's rather the opposite;- the Danes don't want to let go of natural resources on Greenland. Oh well, I'm derailing.