The OP's asking about titration I believe, so initial/final does not apply here.
I think in titration, you start with some acid (or base) and add base (or acid). So you're constantly adding more H+ or OH- s. But yea basically Normality*volume would be the number of moles of H+ or OH- in the acid/base. So if you start with a base, and you want to see what volume of an acid you need to get to the neutral point, you need to add an equal moles of H+ as there # of moles of OH- in solution. So you would have N(base)V(base)=N(acid)V(acid).
This is not the only time you'd use this equation of course.
What Nze mentioned can be used when you have some solution (maybe like 1 M) and you wanna know how much water you should add to make it like 0.1M. Then since you're not changing the number of solute moles, you'd have moles = MiVi= MfVf.