I know in a lot of people's minds, there is a notion that a nuclear power plant could detonate like a nuclear weapon. It's not possible, and I will use the previous few posts to explain why that is.
Recall that neutrons from fission have a very high energy level, about 2 MeV, which equates to a speed of 45 million miles per hour. Neutrons traveling this fast do not interact with Uranium atoms as often as they do after they have been moderated (slowed down) to thermal speed, about 4900 miles per hour.
Nuclear weapons require an absolutely uncontrolled fission reaction. The more fissions that occur before the core is vaporized, the better. This requires that the entire thing take place in microseconds, which also means the neutrons must be fast neutrons. It also requires a VERY dense concentration of fissile material, because fast neutrons don't interact well with atoms.
There are some other techniques used to improve nuclear weapon performance. A neutron reflector is one. It bounces fission neutrons back into the reaction, and makes more fissions possible before the whole thing vaporizes. Another trick is using a tamper - a thick casing to hold the exploding device together for a couple more microseconds, allowing a couple more generations of neutrons to build up.
With a weapon, if the neutrons were thermalized, it would slow down the chain reaction to the point that the uranium or plutonium device would melt or vaporize, rather than detonate. AKA, a "fizzle".
On the other hand, nearly all nuclear reactors are "thermal" reactors, meaning the neutrons are slowed down. This provides fine control of the nuclear reaction, but more importantly allows us to use lower enrichment of Uranium than would be possible in a Fast Neutron Reactor. Fast neutron reactors require enrichment that would be appropriate for weapons, which is why nobody really likes them.
Typical Thermal Neutron Reactors, such as those in power plants, use just 3-5% enriched Uranium, which is too low for a nuclear explosion of the weapons type.
What can occur in a thermal reactor though is a runaway chain reaction that creates enough heat to vaporize metal in the core and create a steam explosion. All nuclear reactors rely on "delayed neutrons" to achieve control. Most fission neutrons are released within 10^-14 seconds following a fission. These neutrons are called "prompt neutrons". That reaction speed is far too fast for humans or electronics to prevent a runaway chain reaction.
Fortunately for us, a small fraction of neutrons are produced by the neutron-rich fission fragments of the split atoms. So... an atom fissions (splits) and releases 2-3 prompt neutrons. Some of the split nuclei decay later and release more neutrons. These are the "delayed neutrons", which can be generated up to 55 seconds after the initial fission event.
The key to controlling a nuclear reactor is to never allow the reactor to be critical on Prompt Neutrons alone. If a reactor does become critical on Prompt Neutrons, the condition is called "Prompt Critical". This is a dangerous uncontrolled reaction, which led to the violent explosions at both Chernobyl and SL-1. It was also done intentionally for the SPERT experiment.
Each of these reactors experienced a prompt criticality event, just like a nuclear weapon. However, because the neutrons were thermalized, which greatly slows down the increase of neutrons, none of these reactors detonated with a nuclear weapon type of blast.
Here is some interesting footage of the Prompt Critical SPERT reactor experiment:
Below is the account of the SL-1 accident, where the first operator fatalities took place. Move it to the 1:00 minute mark to avoid the intro. SL-1 might be the reason nobody allows the US Army to play with reactors any more :)
And lastly, Chernobyl. The worlds biggest Dirty Bomb.