There are three kinds of waste: 1. Waste from extraction of uranium ores. This part is relatively insignifcant; 2. Enrichment waste. Most (all?) power-generat

There are three kinds of waste: 1. Waste from extraction of uranium ores. This part is relatively insignifcant; 2. Enrichment waste. Most (all?) power-generating nuclear power plants use U235 as fuel. Mined uranium is primarily U238 with low amounts of U235. This metal needs to be enriched, which is to say the percentage of U235 needs to be made higher. This is really the only difference between reactor-grade Uranium and weapons-grade Uranium (ie the percentage of U235). These are isotopes so are chemically identical. So how do we do it? We convert it to a gas and put them through a series of centrifuges. These centrifuges will effectively increase the concentration of U235. How we do this is with Uranium Hexaflouride (UF6). UF6 is a significant waste byproduct that requires storage. There are processes to make this less toxic (eg UF6 -> UF4) but they aren't really economic, at least not yet; and 3. The reactor fuel itself creates waste in the form of radioactive fissile products and fuel decay products. Every now and again the fuel rods need replacing. This is an expensive and highly-skilled process done by the NRC. Those byproducts need to be stored or disposed of. This article is talking about this form of waste, specifically.