Several things caused the disaster at Chernobyl. The plant was not properly designed, and could only be run with very specific instructions. The operators of the plant failed to properly follow these instructions, and some scientists conducted a highly risky experiment that led to the explosion.
The scientists decided to conduct the experiment, and had to remove safety and cooling equipment in order to do so.
Eventually, pressure on the reactor's roof blew it away. Everything inside, including molten uranium, burning graphite, and radioactive ashes were emitted into the atmosphere.
This was not a nuclear explosion. There was no chain reaction or explosion like that in an atomic bomb. However, the amount of radioactive material released was ten times that caused by the US atomic bombing of Hiroshima.
Radioactive fallout spread throughout Europe. It hit Poland, Germany, Belgium, France, and Holland, then shifted towards the Balkans and Italy.
It is impossible to tell just how many people were affected by the Chernobyl explosion. A British report estimated that the radioactivity will give 2300 people cancer, though others think the number is much higher.