When the salt molecules dissolve in the water, they do not attach easily to the solid ice. There are fewer water molecules in the liquid because the some of the water has been replaced by salt. This means that the number of water molecules able to be captured by the ice (frozen) goes down, so the rate of freezing goes down.
The rate of melting of the ice is unchanged by the presence of the salt, so melting is now occurring faster than freezing. So the ice eventually melts.
The rate of melting of the ice is unchanged by the presence of the salt, so melting is now occurring faster than freezing. So the ice eventually melts.