As you have realised, the boiled solution of red cabbage can be used as an acid/base indicator. In other words, you can use this solution to distinguish an acid from an alkaline or neutral solution.

An acid/base indicator is a weak organic acid or base. Its dissociated form differs from the nondissociated form by its color change as conjugated base or acid. Due to this fact, the color of the solution depends on the solution acidity (pH <7) or alkalinity (pH>7). When you use red cabbage in salads you can verify that it acquires a red color when you add vinegar (acid). In contrast, if in the preparation of a red cabbage soup you use tap water, you can verify that the solution becomes blue. This because the tap water is a weak base. Try it!