A nuclear reactor is a device used to initiate and control a sustained nuclear chain reaction. Emmett Brown used one in his DeLorean time machine to generate the 1.21 gigawatts of electricity needed to power the flux capacitor, which was necessary for time travel.
In a nuclear reactor, heat from nuclear fission is cooled with a nuclear coolant, usually water, but sometimes gas, a liquid metal, or molten salt. The cooling function of the DeLorean was handled by the rear louvers, which would expel a cloud of cold air as the time machine vented.
By 2015, the Mr. Fusion home energy reactor allowed nuclear power for individual homes, in a compact unit which housed a tiny nuclear reactor. Doc adapted one of these devices to replace the nuclear reactor in the DeLorean time machine.
In 2045, a nuclear holocaust is caused by Griff Tannen. He uploaded a virus to the popular social network created by GriffTech, ThingMeme. It was supposed to flash the word butthead on every object on Earth, but instead, the virus causes a short circuit in the Mr. Fusion network, causing a nuclear explosion in all one hundred million of the tiny nuclear reactors present in every unit. Doc traveled back in time to prevent the invention of the Mr. Fusion, which prevented the 2045 nuclear holocaust from occurring.