A permanganate solution is usually purple in colour. Permanganate contains the manganate ion (MnO₄⁻) and manganese has an OS of +7. However, in an acidic solution, the permanganate (VII) ion gets reduced to the manganese (Mn₂⁺) ion which has an oxidation state of +2 and is colourless.
Since Potassium permanganate (KMnO₄) is quite an unstable compound, it tends to decompose in the presence of Ferrous sulphate (FeSO₄). This changes the colour of the solution from purple to colourless. The FeSO₄ gets oxidized to Fe₂(SO₄)₃ as KMnO₄ acts as a good oxidizing agent in an acidic medium.