Molarity is the number of moles of solute per liter of solution (common measurement of chemical concentration), while normality is the measure of concentration equal to the gram equivalent weight per liter of solution. Normality and molarity are both measures of concentration in chemical solutions.
For example,
A 1 M solution of H2SO4 contains 1 mole of H2SO4 per liter of solution. H2SO4 dissociates into H+ and SO4- ions in water. For every mole of H2SO4 that dissociates in solution, 2 moles of H+ and 1 mole of SO4- ions are formed. This is where normality is generally used.
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.
N = M*n
where n is the number of equivalents