OK, this means the valve is not shutting tight . appliancepartsimages.com/dbImages/00002079/00626272.jpg" alt=""/>these are electronic and when they get older they tend to stick open a bit and allow water to get by causing your issue, these are easy to change and its located where the water line from the house connects to the refrigerator. below is a link where you can order this, if the ice is a lot you can shut the water supply off behind the refrigerator until the part comes in.
link for part.... http://www.repairclinic.com/PartDetail/Water-Inlet-Valve/D7712603/3089 just click on that blue link to order the valve. thanks and s best wishes, Bryan