Potassium permanganat is used as an oxidizing agent to determine the hydrogen peroxide amount in a solution. Hydrogen peroxide reduces the permanganate to a colorless product. This is a great example for a redox reaction.

2 KMnO₄ + 3 H₂SO₄ + 5H₂O₂ = 2 MnSO₄ + K₂SO₄ + 5O₂ + 8H₂O

or less confusing

5 H₂O₂ + 2MnO₄^- + 6H+ = 5O₂ + 2Mn²⁺ + 8H₂O

Manganese can exist in all oxidation states from +2 to +7. Manganese II forms salts with all common anions. They are mostly light pink in color. Manganese VII is found in the intense purple colored permanganate ions MnO₄^-. As long as you have hydrogen peroxide in your solution, the permanganate will always be reduced to a clear solution. But as soon as the hydrogen peroxide is gone the intense purple color of the permanganate will be visible.

Note: It is important that the hydrogen peroxide solution is acidic. The hydrogen ions take part in the reaction as a reactant. The protons are needed to form water. It is also important to use sulfuric acid and not hydrochloric acid because the permanganate is such a powerful oxidant, it would oxidize chloride ions to form chlorine.