I saw a reaction by chemicalforce on YouTube where he decomposed $\ce{H2O2}$ into $\ce{H2O}$ and $\ce{O2}$ using potassium permanganate. The permanganate is a catalyst in the reaction.

I am wondering if this decomposition occurs because the initial $\ce{H2O2}$ decomposition reacts with the $\ce{KMnO4}$ and reproduces $\ce{H2O2}$ which then again decomposes?

How is the permanganate a catalyst?