5 K2S2O8 (aq) + 2 MnSO4 (aq) + 8 H2O (l) → 2 KMnO4 (aq) + 4 K2SO4 (aq) + 8 H2SO4 (aq)
This is an oxidation-reduction (redox) reaction:
2 MnII - 10 e- → 2 MnVII (oxidation)
10 SVII + 10 e- → 10 SVI (reduction)
MnSO4 is a reducing agent, K2S2O8 is an oxidizing agent.