Although it can seem a unusual question it simply requires to have understood the basis of a titration.
First of all, what is a pH indicator? It is simply an acid-base compound whose acid and base form present different colours. This makes these compounds often used to determine the pH of a solution - and to determine the concentration of an unknown acid or basic solution.
Let’s take an example: the titration of a hydrochloric acid solution by a sodium hydroxide solution with BBT (bromothymol blue). A few drops of BBT are added to the acid solution which takes the colour of the BBT acid form – ie yellow. The hydroxide sodium solution is then added dropwise to the acid solution. The hydroxide ions reacts with the oxonium ions of the acid solution to give water according to the equation: H3O+ + HO- = 2 H2O. As long as there are H3O+ ions in the reaction mixture the hydroxide ions will be neutralized: the solution will stay acidic and keep the yellow colour of the BBT. However oxonium ions are also consumed, and the reaction basicity increases slowly, until all the oxonium ions have been consumed: the equivalence is reached. Now what is the consequence on the solution colour? The acid and basic forms of the colour indicator are in equilibrium, therefore the colour is in-between the acid and the basic colours. In the case of BBT the solution will turn green. If hydroxide ions are added beyond this moment, there won’t be any more acid species to react with them and the pH of the solution will increase. It will therefore takes the colour of the basic form of the pH indicator – in this case blue.
Now why is BBT a good pH indicator for this titration? The key point is that the colour change occurs when the equivalence is reached. The colour depends on the dominance of either the acid or the basic form of the indicator at a given pH. This information is given by the pKa of the acid-base couple. It is usually assumed that at pH = pKa – 1 the acid form dominates whereas at pH = pKa + 1 the basic form dominates. Therefore to have the colour change when the equivalence is reached the pH then must be as close as possible of the pKa of the indicator. Going back to the example, the pH of the titration of a strong acid by a strong base is 7 – which is also the pKa of BBT.