For example, one important fission product in a nuclear reactor is xenon-135, which is produced from the decay of iodine-135, which is a product of nuclear fission. When you run the reactor, it produces iodine-135, which has a half-life of 6.6 hours, producing xenon-135.
Xenon-135 is a "nuclear poison." It is the the strongest known neutron absorber, and it absorbs neutrons in the reactor that would otherwise be used for fission. While the reactor is operating normally, the reactor neutrons will "burn off" the xenon-135, and the fission products will produce new xenon-135, and you can run these reactions in equilibrium.
If you turn a reactor off, the xenon-135 builds up to higher levels--remember, takes hours for the iodine-135 to decay. Because xenon-135 inhibits the reactor, you have to either wait for the xenon-135 to decay (9.14 hour half-life) or you have to pull out the control rods to compensate.
The Chernobyl operators turned the reactor off (not on purpose), xenon-135 built up, and then they pulled out the control rods to start it back up. When the reactor finally started up, the xenon-135 was burned off by the neutrons in the reactor, but this happened quickly, and the control rods were still out.