For starters, the roof was build without fireproof materials and the reactor hall did not have it's concrete "bunker" around it that all Western reactors have. If it had, the disaster would not have nearly been as large.
Then the human error. The main authorities wanted to know if the back-up coolant pumps go online rapidly enough after the main pump has been shut down.
The night-shift that was tasked to carry out this experiment was ill prepared. When one of the operators reduced the power of the reactor to start the test, power was reduced so much that the reactor shut down. The foreman during that night insisted that they removed all the control rods - needed to control the nuclear reaction - so the reactor would turn on quickly again and their test could be continued.
This + another whole bunch of poor decisions caused a massive steam explosion once the coolant pump was shut down which ruptured the reactor vessel, the generator halls and the reactor hall.
There's a good documentary, Zero hour, made by Discovery, which explains the lead-up to the disaster. They even filmed it in Reactor 3 at the Chernobyl plant. Otherwise I would point you to Wikipedia.
There was a power output surge, and when an emergency shutdown was attempted, a more extreme spike in power output occurred, which led to a reactor vessel rupture and a series of explosions. These events exposed the graphite moderator of the reactor to air, causing it to ignite. The resulting fire sent a lot of highly radioactive smoke fallout into the atmosphere, thus letting radiation travel into the nearby towns and affecting the citizens.
In the 80's there was a nuclear reactor in Ukraine and it cracked and radiation leaked into a industrial city forcing evacuation of the city.
It was caused due to pour maintenance. America tried to help but communist Russia and Ukraine would not let us.
Someone got a 25 killstreak there.
