3 KClO3 (aq) + 2 KMnO4 (aq) + H2O (l) → 3 KClO4 (s) + 2 MnO2 (s) + 2 KOH (aq)
This is an oxidation-reduction (redox) reaction:
2 MnVII + 6 e- → 2 MnIV (reduction)
3 ClV - 6 e- → 3 ClVII (oxidation)
KMnO4 is an oxidizing agent, KClO3 is a reducing agent.