Icicles dangling from a thick blanket of snow on a roof are the backdrop to an idyllic winter scene. That same pretty picture of ice might cause an ugly reality for the residents inside the home.
The weight of the ice bearing down on the gutters backs up to the point where it melts into the home, encouraged by heat emanating from the interior of the house. If you cannot remove the snow from the roof, ice dams can block water backing it up rather than allowing it to run off of the roof.