Salt water fish actually drink the salt water, excrete the salt, and are left with unsalted water in their body; they do this because the sea water, through the process of osmosis, draws out water from the body.
When they are placed in fresh water, they continue to drink the water, but since the water is now less saline that the fish, water is no longer being drawn out, and in most cases (especially if the transfer was too quick), will start absorbing water, hence they will typically die.
