An ice dam is a ridge of ice at the roof's edge that traps melting snow, which then backs up under the shingles and leaks into the house. They're a symptom of heat escaping into the attic.
Why they form
Heat leaking from the house warms the roof and melts the snow on it. The meltwater runs down to the cold overhang, refreezes, and builds a dam. Water pooling behind the dam works its way under the shingles.
The real fix
Ice dams are fixed from inside, not on the roof: air-seal the attic floor so warm air can't rise into the attic, add insulation to keep the attic cold, and ensure good attic ventilation so any heat is carried away. A cold roof doesn't melt snow unevenly.
Short-term relief
Raking snow off the lower roof after big storms reduces the meltwater available to form a dam. Never chip at ice on the roof — you'll damage shingles. Heated cables are a band-aid, not a cure.