Why does salt make ice melt?
The short answer
When salt dissolves in the thin layer of water on ice, it lowers the temperature at which that water freezes. The balance between melting and freezing shifts toward melting.
What happens on the surface
There is usually a very thin layer of liquid water on ice. Salt dissolves in it, and salt water does not freeze at the same temperature as fresh water. If the surroundings are warmer than the new freezing point, more ice changes into liquid water.
It does not work without limits
If the air is extremely cold, salt water can still freeze. There is also a limit to how much salt can dissolve, so adding more salt does not make ice melt forever faster.