There several issues that can lead to Ice Dams forming on your roof. One very common cause is a lack of insulation in the attic space, this allows warm air from inside the house to escape into your attic space & warm the underside of your roof decking. This heating leads to melting of the snow on your roof, when this melting snow then re-freezes it causes water to back up create the leak. Many homes built prior to 1990 may be under insulated.
Another cause leading to the creation of Ice Dams is under utilization of intake/exhaust venting in your attic space.