The very short story is that unlike with something like gasoline combustion, where the energy output basically happens nearly instantaneously, a nuclear fission event releases energy both directly (from the fissioning) and indirectly (from the subsequent radioactive decay of the fission products).

This indirect energy output is small in comparison to the reactor's output, but a small percentage times a very large power output is still sufficient to meltdown a reactor (and boil away the coolant in the process) if there's no way to remove the heat being generated.

Imagine what you'd have to do with a car engine if every car trip of 4 hours or more produced 4% power output in the form of heat for the next day after your trip was over.

Once the control rods are in, the reactor is losing more energy than it is producing and will eventually cool down. However in many old (e.g. 60's era) designs including Chernobyl and Fukushima, the reactor is losing that heat via active water cooling. If you turn off those heat pumps, then the core is still energy-positive even with rods inserted.

In Chernobyl the core literally blew up, so it's a different situation. But in Fukushima the pumps lost power and so even though the control rods were fully inserted, there was a real risk it might get hot enough to melt down anyway. That was thankfully avoided.

Reactor designs differ, and they tend to have a large number of emergency backup and contingency plans. Here's a decent overview for a typical reactor: https://interestingengineering.com/nuclear-meltdown-what-wou... (scroll down to "Preventing a nuclear meltdown").

TL;DR: the control rods slow the reaction, but the fuel rods are still hot, and the space is enclosed (to prevent radioactive material from casually escaping) so it gets hotter and hotter without intervention. If the fuel rods get hot enough they start melting, which produces hydrogen, which can explode.