In an ideal world, the colour change would happen when you mix the two solutions together in the correct proportions according to the equation (often just called 'equation proportions'). When the indicator changes colour, this is often described as the end point of the titration. When you carry out a simple acid-base titration, you use an indicator to tell you when you have the acid and alkali mixed in exactly the right proportions to 'neutralise' each other.
This page describes how pH changes during various acid-base titrations.
