Since Normality equal to the molarity times the number of equivalents per mole of solute, normality is (theoretically) easier to work with for things like titrations, etc where equivalents are important.
Like, 10 mL of 0.1 M HCl (0.001 mol) needs 10 mL of 0.05 M Ca(OH)2
- which is 0.1 N with respect to OH-
- this way, the numbers work better.
Of course, sometimes it's easier the other way. It's like temperature. Celsius, Kelvin, Fahrenheit, Rankin...Why don't we just use one eh