After watching the TV series Chernobyl I am struggling to understand why steam in a reactor core would increase the rate of the nuclear reaction. My first guess would be that liquid water would accelerate the reaction as it is used as a moderator in other reactors.
The reactor type installed in Chernobyl (Wikipedia: RBMK) uses graphite as moderator. The water also moderates, but its effect is proportionally much less important than in a water-moderated reactor. This means a steam bubble forming results in only a small reduction in moderator efficiency but a large reduction in neutron absorption, thereby increasing the fission rate. This behaviour is referred to when the reactor is described as having a high positive void coefficient (the link goes to the subsection of the above Wikipedia article discussing this).
Liquid water both moderates and captures neutrons. Steam (gaseous water) does neither to any effect. At the initiation of the "pump run-down test" there was very little steam production in the fuel channels (thermal power <7%). An expected consequence of the "test" was a drop in Steam Separator (and reactor coolant) pressure as the #8 Turbine-Generator valves opened to power Reactor Coolant Pumps during a (simulated) loss of plant power. This caused the now super-saturated water in the core to boil as the pressure decayed.
Because the coolant was very near saturation temperature throughout the entire system, voids formed throughout the entire core almost simultaneously. Neutrons that would have been absorbed by water milliseconds earlier were moderated by the graphite and causing more fissions... causing more heat, more steam, more neutrons, and so on.
liquid water is more efficient at absorbing neutrons than moderating them compared to graphite. As nearly ALL of the control rods were fully withdrawn, only Xenon and liquid water were limiting the reactor (by absorbing neutrons). Steam forming in the coolant channels stopped absorbing neutrons, but the graphite continued to moderate them so the fission efficiency actually improved as voids formed. The term 'Positive Void Coefficient' is somewhat misleading... In an absolute sense, gaseous steam is 'Less Negative' than liquid water in a graphite moderated reactor.
The core configuration and particularly the coolant thermal conditions were such that it all makes sense, predictable with hindsight (or foreknowledge). the HBO mini-series short changes the accident sequence-of-events (my opinion - and I would think that). The "Test" preparation, delay, and finally, the foolish execution; set the stage and triggered the unimaginable.
How the void coefficient, normally a small influence in the reactor's operation and power calculations, came to trigger an order-of-magnitude runaway power excursion was not portrayed very clearly in the mini-series. The "test" was the motivator for virtually everything leading to the event, and technically kind of interesting in its own right. I wish there was a scene in the pump room as the additional circulating pumps spooled up with appropriate sound and pipe motion.