Today, Greenland becomes a self-ruling country, responsible for its own judicial affairs, policing, and natural resources (Denmark will continue to control finances, foreign affairs, and defense).
The flag (native term in the title) succeeds the Dannebrog, the white cross on a red field that has symbolized Denmark since the 14th century. Original plans were to continue the cross motif, changing the colors to green and white, but the committee finally selected this "horizontal bicolour of white and red, with a counterchanged disk slightly off-centre towards the hoist."
More details at Wikipedia.