Ice Dam Causes
Very simply - snow and heat. Ice dams are formed when snow melt refreezes at the eaves (gutters) and in the valleys. Causes for snow melt can be heat loss from the house, solar radiation (sun's rays) and temperature fluctuations above and below freezing. The cycles of melting and freezing cause a build up or DAM. This dam traps water behind it. The trapped water builds until it finds a way into the house.
Ice dams are not caused by gutters or gutter protection.
Some gutter protection tends to display the ice dam sooner. Reverse curve or 'helmet' style gutter toppers are fabricated from thin metal which cool very quickly. Their placement above the gutter means you see the ice forming earlier. Some attempts have been made to heat these covers, usually with little success. The metal is just too thin to be a good conductor of heat.
Icicle formations are often associated with ice dams. Some of the dammed water flows over the top of the dam and refreezes as icicles. Ice dams cause property damage and can pose a risk to people as well. Falling icicles (ice weighs @ 60 lbs. per cubic foot) can hit people, cars, lower structures, etc. Leaking water damages drywall, lowers the effectiveness of insulation (making the problem worse), and can lead to rot and mold growth. Repeated ice dam cycles weaken roof structures, loosen gutters, damage shingles, and cause a variety of other problems.