A strong acid (H⁺) in the beaker is neutralized drop by drop by a strong base (OH⁻) delivered from the burette above: H⁺ + OH⁻ → H₂O. Every drop consumes acid and base in a 1:1 mole ratio, which is why the reaction is called neutralization — the products are just salt and water.
Before the equivalence point (moles base added = moles acid present), leftover H⁺ keeps the solution acidic and pH stays low. Exactly at equivalence the acid and base have exactly cancelled and pH jumps sharply through 7. Past it, excess OH⁻ takes over and pH climbs toward strongly basic.
An indicator is a weak dye whose own protonation state — and therefore color — flips over a narrow pH window. Phenolphthalein is colorless in acid and turns pink only after ~pH 8.2, which is why it is the classic titration indicator: it stays colorless right up to the equivalence point, then snaps to pink almost exactly when the reaction completes.