In the most common case, the water simply backs up and flows under the shingles. From the attic, it could move into exterior walls or through the ceiling insulation and stain the ceiling finish. Since most ice dams form at the lower edge of the roof, there is obviously a heat source warming the roof elsewhere. This heat is primarily coming from the house. In rare instances, solar heat gain may cause these temperature differences.
Conduction is heat energy traveling through a solid.
A good example of this is heating a cast iron frying pan. The heat moves from the bottom of the pan to the handle by conduction. If you put your hand above the frying pan, heat will reach it by the other two methods. The air right above the frying pan is heated and rises. This is heat transfer by convection .