The Soviet Union and the nuclear power plants in 1986
The Soviet nuclear program was being developed. At the time of the accident, they had 43 reactors, providing the power of 26 billion watts (26 gigawatts). On the other hand, another 34 reactors were under construction, to provide 36 billion watts (36 gigawatts). It is interesting to note that, already at that time, the Soviets switched to the pressurized water reactors (PWR) rather than the RBMK. Maybe it was already an admission of obsolescence RBMK reactor ...
What is a nuclear reactor?
In summing up quickly, a nuclear reactor which is a kettle, making boil water, thus produces steam, and the steam is then used to drive the turbines that will spin the alternators which will produce electricity. A nuclear power plant operates in exactly the same way as a "conventional" power plant, except that the energy to produce steam is supplied by the thermonuclear fission rather than coal, gas or fuel oil.

A very simplified diagram of a nuclear power plant
Overall, all reactors operate on the same principle, quite simple indeed: neutrons break uranium atoms. This action produces heat and new neutrons which will help to maintain the reaction. The heat produced during the reaction will warm the water to boil and steam generating, and the energy of this steam will drive a turbine coupled to a generator that produces electricity.
The high-speed neutrons can not sustain a chain reaction. Because of this high speed neutrons would have little chance of reaching an atom of uranium. Also, in all reactors, it uses a feature called "moderator", whose goal is to slow the neutrons to enable them to reach their target, the atoms of uranium. This moderator can be of the light water (our domestic water H2O), the heavy water (a variety of water, with high concentration of deuterium, an hydrogen isotope, with a density of about 1.1), graphite as in the case of RBMK reactors. Almost all Western reactors use of the light-water or heavy water.
Of course, we must be able to control the reaction in the "kettle." A reactor is stable when it consumes so many neutrons it produces. If the reactor needs more neutrons than it produces, it will stop, and if it produces more neutrons than it consumes, the power increase, as more uranium atoms will be broken. To regulate the flow of neutrons, it uses "control rods", made of highly neutron absorbent material, such as boron. When these control rods are inserted in the reactor core, they absorb neutrons which break less atoms of uranium and power decreases. On the other hand, if these control rods are taken away from the reactor, the neutrons will no longer be absorbed and power increases.