Theory

The potassium permanganate oxidises the glycerol to carbon dioxide and water (hence the steam) and is itself reduced.

Extensions

The reaction does not appear to work if crystals of potassium permanganate are sprinkled into glycerol.

Further details

Fine crystals of potassium permanganate appear to work much better than larger ones, so grind large crystals in a mortar and pestle. Old glycerol can be ineffective, possibly due to absorbing water. To remedy this, heat old glycerol to boiling then allow to cool, or dry over calcium oxide.


Safety

Wear eye protection.
The residue from the reaction can be washed down the sink with plenty of water.