A salt is an ionic compound which is made up of two groups of oppositely charged ions.

The overall compound of a salt compound must have an overall electrical charge of 0.

Ammonium sulfate, (NH4)2SO4, can be made by the reaction of ammonia, NH3 with sulfuric acid, H2SO4. 

Therefore, ammonium sulfate is described as a salt because the hydrogen ions, H^+, in sulfuric acid have been replaced by ammonium ions, NH4^+

And note: the charge of ammonium sulfate balance - NH4 has a +1 charge and SO4 has a 2- charge, therefore in the compund there are two lots of NH4+ [(NH4)2], to cancel out the 2- charge of the SO4 to equal 0.