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).
Water is a good shielding material for neutrons. Moderating the neutrons will slow the reaction rates. When steam forms, it forms from the water used for moderating hence decreasing the amount of water. This decrease in water will speed up the reaction rates.