In large quantities salt in soil will kill grass and other plants. Rain will eventually flush small amounts of salt away, but large doses of salt will alter soil chemistry to the extent that it can no longer support grass.
Salt destroys soil's natural bacteria and absorbs water while extracting minerals. When enough salt saturates the ground, grass, weeds and other plants no longer have enough nutrients to survive.
Grass dying from salt saturation will appear wilted even when the surrounding soil is damp. Excessive salt will give soil a cracked appearance, and you may see salt crystals on top of the cracked ridges.
Salt water harms grass and soil, contaminates the community water supply and damages trees. These effects linger because large quantities of salt in the ground are slow to evaporate.