Definition: Normality is a measure of concentration equal to the gram equivalent weight per liter of solution. Gram equivalent weight is the measure of the reactive capacity of a molecule.
The solution's role in the reaction determines the solution's normality.
For acid reactions, a 1 M H2SO4 solution will have a normality (N) of 2 N because 2 moles of H+ ions are present per liter of solution.
For sulfide precipitation reactions, where the SO4- ion is the important part, the same 1 M H2SO4 solution will have a normality of 1 N.