Mass balance is making sure nothing you had originally is disappearing.
For example, take HF (a weak acid)
If the molarity is 0.1 M, that means before anything dissociated, there was 0.1 mol of HF per liter.
In the end, after dissociation, there will be HF in the water and also F- ions. And the concentration of both those put together will be the concentration of HF that you originally put in (after all, it can't go anywhere, or appear out of nowhere)
So, the concentration of HF initially is the concentration of HF in solution plus the concentration of F- in solution
I.e. 0.1 M = [HF] + [F-]
and you can extend this to substacnes if you like...acids with 2, 4, 6 protons...ions that form complexes...you just have to account for all reactions, dissociations, etc.
Good luck!