Many people have seen mushroom clouds from nuclear explosion and this is what comes to mind when they hear nuclear reactor.

However, a nuclear explosion can’t happen in a nuclear reactor.  A nuclear explosion involves a system that compresses nuclear material and holds it together long enough for a significant portion of the fuel to react.  A nuclear reactor lacks the necessary confinement for that to happen so no, your friendly neighborhood nuclear reactor can’t initiate a nuclear explosion.

But boiling water and pressurized water reactors can explode. There are two ways a nuclear reactor can explode.  Boiling water reactors operate at 70-80 atmospheres and pressurized water reactors at 150-160 atmospheres.  These reactor designs are the bulk of existing commercial power reactors presently in operation for the purposes of generating electrical energy.

If there is a leak in the plumbing or the reactor vessel, all of that water can flash to steam instantly resulting in sudden and substantial damage.

The other type of explosion that can happen is the result of using water for a coolant.  During normal operation neutron bombardment breaks some water molecules apart, this generates a low level of hydrogen and oxygen that is normally combined back into water through the use of a catalytic re-combiner. In normal operation this hydrogen and oxygen does not normally represent a threat.

If for some reason the reactor overheats, the zirconium cladding used in the fuel rods can react with steam, from the now vaporized reactor cooling water, releasing hydrogen at a rate that exceeds the re-combiner’s capacity.  When this happens hydrogen can build up until an ignition source results in detonation.  This generally results in an violent explosion. This is the type of explosions experienced at the Fukushima reactor site.

There are newer reactor designs not subject to these failure modes, in fact not subject to any dispersion event.  These are fast spectrum molten salt reactors.