Everything, including yourself, is made of atoms. All atoms have nuclei. You have many atomic nuclei inside yourself since you are made of atoms. The simplest nucleus is one proton. That would be a hydrogen atom. An oxygen atom has 8 protons and either 8, 9 or 10 neutrons in its nucleus. All other nuclei also have neutrons. Uranium has 92 protons and either 143 or 146 neutrons. If it has 143 neutrons it is U235. If it has 146 neutrons, it is U238. Nuclear fuel is only 2% to 8% U235, the kind that fissions/divides, providing energy. The rest is U238 that doesn't fission. A nuclear reaction happens when a neutron is captured by a nucleus. If a U235 nucleus captures a neutron, the nucleus and the atom split
approximately in half and 3 more neutrons are released because the 2 smaller nuclei don't need so many neutrons. If a U238 nucleus captures a neutron, it ejects an electron and the neutron becomes a proton. The U238 thus becomes Plutonium 239. [In a power plant, Plutonium 239 [Pu239] quickly captures another neutron and becomes Pu240. Pu239 makes good bombs but Pu240 bombs fizzle and are militarily useless.] Plutonium is fissionable, which means that plutonium is a good fuel. If you add Thorium to the fuel, you can make more fissionable uranium. If a Thorium atom nucleus captures a neutron, it ejects an electron and the neutron becomes a proton. The Thorium atom thus becomes U233. U233 is fissionable.
Depending on the design of the reactor and the mix of the fuel, the fuel % in the reactor can either grow or shrink. It is kind of like the fuel gauge can go either up or down, but it is more like the reactor can run hotter or cooler over time. The temperature is kept constant by adjusting the control rods. A breeder reactor is a reactor designed to make the fissionable part of the fuel load grow rapidly. Normally, fuel is left in the reactor for about some number of years, or some percentage of the fuel is replaced each year. The reprocessing step sorts out the fuel and puts the percentage of fissionable fuel back to the starting percentage. In the process, plutonium may be removed and either wasted or used as fuel. If we add thorium to the fuel, we can make more uranium than we put in. Since the earth contains more than twice as much thorium as uranium, it would be wise to make thorium into uranium. By reprocessing nuclear fuel, we get an enormous, many centuries long fuel supply without doing much mining. Only minute amounts of un-enriched uranium or thorium need to be added to lower the percentage of fissionable fuel. The products of fission are also removed when fuel is reprocessed. These are just other atoms that are no longer useful as fuel. The quantity is very small. We should reprocess fuel to keep the fuel load at the correct percentage of fissionable fuel for the particular reactor design. Instead, we go through the expensive process of making more "virgin" fuel for each new fuel load. This greatly increases the price you pay for electricity. We are not reprocessing nuclear fuel for political reasons.