What was the cause of the Chernobyl nuclear disaster?

After the steam explosion which blew the top of the reactor off, the graphite moderator was exposed to air, and as it was hot enough it started to burn. Decay heat from the fuel would have contributed to the high temperature as well. Graphite burns well in air, as barbecues demonstrate.

See Wikipedia 'Chernobyl disaster' for more information on the development of the disaster.