What do we mean by #"back titration"#?

In titration, when your titrant (e.i. NaOH) is present in excess amount (i.e. phenolphthalein indicates a deep hue of purple instead of very light pink) a standard solution of strong acid (e.g. HCl) must neutralize the excess amount of your titrant.
This is done by titrating your solution, containing your excess amount of base with your standard acid until the solution gives a very light shade of pink, which is your phenolphthalein end point.
Back titration is done done using strong acids or strong bases. This to assume complete dissociation in solution and a 1:1 ratio of reaction between your OH & H30+.

Suppose we had a refractory metal oxide that only reacted slowly with acid. Direct titration with acid would be problematic in that we might add the titrant too quickly for equilibrium to be established.

An alternative strategy, would be to #(i)# add a known quantity of acid in EXCESS, wait for the reaction to go to completion (perhaps we would wait overnight), and then (after reaction is complete) back titrate the acid in excess with standardized base #(ii)#. Because we know both the molar quantity of the acid added #(i)#, and we know #(ii)# the quantity of the acid left unreacted, #(i)# #-# #(ii)# relates to the quantity of the metal oxide, whose molar quantity we approached indirectly. Is this clear?