
Ice Dams happen when you have snow on the roof and the heat that escapes form inside your house / attic melts the snow.
As it melts, water runs down the roof, and when it gets to the edge (eaves) which are unheated, it once again freezes.
As more and more water freezes along the eaves, ice builds up, creating ice dams. As even more water runs down, it now has nowhere to go, so it backs up under the shingles, and leaks into your roof.
In general, the steeper your roof, the more thick a dam would have to be to cause damage. Conversely, the flatter your roof, the more susceptible it will be to ice dams.
The resulting damage can be quite extensive and costly to repair. It ranges from torn off gutters and falling shingles to peeling paint, ruined flooring and stained ceilings, if the water gets into the house.