I've never really been able to learn much about the Three Mile Island disaster and i've been curious to know what the chain of events both in the plant and in the wider context contributed to it, what happened in itself, and how it was responded to by the U.S government, local government, and if at all, by the nuclear power industry.
I don't know if this is really a history question, this is more of a nuclear engineering question. This might be better placed in /r/nuclearpower
The World Nuclear Association gives a thorough overview of it, the response to it, etc.:
Here's a summary.
Basically what happened was there was a minor malfunction in the secondary coolant circuit which caused the coolant temperature to rise. The reactor began an automatic shutdown sequence, so one of the valves opened to vent pressure. However the valve failed to close so most of the primary coolant drained away, but the indicator didn't actually give the valve's position so they didn't know it was stuck. As a result replacement water was continually injected into the tank. Not knowing all the primary coolant had drained out, they thought the pressurizer was malfunctioning so they cut off the replacement water flow. Steam built up which caused the coolant pumps to vibrate, so they shut down the pumps which forced cooling of the core (still thinking the whole thing was full of coolant water). The fuel rods heated up, were damaged, and released radioactive material into the coolant.
Eventually shutting an additional valve stopped the loss of coolant. They pumped water in to try and replace the coolant, but pressurized steam blocked coolant from getting into the system. The gases eventually ended up being forced into an auxiliary tank once the pumps were restarted, and they transferred the gases into a waste gas decay tank. The compressors leaked however, which released some radioactive noble gases (xenon) into the environment, but HEPA filters and other safeguards prevented the spread of radionucleides.
Dosage was roughly the equivalent of eating a banana to those most expose to the incident. In other words, harmless.
However it had a pretty major impact on the nuclear industry. It spurred the Anti-Nuclear movement (which interestingly enough was founded by fossil fuels, long story there) and the US changed its policy regarding nuclear construction, stopping new construction.
Three Mile Island caused us primarily to overhaul the safety standards of the industry. Nuclear power in the west has always been exceptionally safe, and many of the new standards are now part of the reason why construction of new plants is so ridiculously expensive (among other factors).
Interestingly a recent study actually showed that had construction not stopped, the US would have eliminated all of its coal and natural gas by 2015, becoming totally emissions-free in its electricity sector, and could already have been on its way to decarbonizing manufacturing and shipping.