An acid-base indicator is usually a weak acid or weak base whose protonated and deprotonated forms have different colors.

Represent a weak-acid indicator as

$$\mathrm{HIn+H_2O\rightleftharpoons H_3O^+ + In^-},$$

where $\mathrm{HIn}$ and $\mathrm{In^-}$ have visibly different colors.

Its equilibrium constant is

$$K_a=\frac{[\mathrm{H_3O^+}][\mathrm{In^-}]}{[\mathrm{HIn}]}.$$

Rearranging in Henderson-Hasselbalch form gives

$$\mathrm{pH}=pK_a+\log\frac{[\mathrm{In^-}]}{[\mathrm{HIn}]}.$$

A visible color transition occurs while both forms are present in comparable proportions. As a useful approximation, the transition interval spans roughly

$$pK_a-1\lesssim\mathrm{pH}\lesssim pK_a+1.$$

Below this range the protonated color dominates; above it the deprotonated color dominates.

In a titration, the equivalence point is the stoichiometric point determined by the reaction. The endpoint is the experimentally observed signal used to estimate that point, such as an indicator color change. They are not identical concepts.

A suitable indicator has its color-change interval within the steep pH-change region around the equivalence point. For a strong-acid/strong-base titration, the pH jump is broad enough that several indicators may work. For a weak-acid/strong-base titration, the equivalence point is basic, so an indicator whose transition occurs in the corresponding basic range is preferable to one centered near neutral pH.

An indicator is added only in a small amount so that its own acid-base equilibrium does not materially alter the solution being measured.

The best indicator is therefore selected from the shape and equivalence-point pH of the titration curve, not from a rule that every acid-base titration ends at pH 7.