When a uranium-235 nucleus splits, the two daughter nuclei are not usually stable. Their combination of protons and neutrons is unbalanced, because they have too many neutrons for their size. This means the products of nuclear fission are radioactive.
Each daughter nucleus decays, often by emitting beta particles and gamma radiation, until it reaches a stable form. Some of these products have short half-lives and decay quickly. Others have long half-lives and stay radioactive for thousands of years.
This is why the used fuel rods taken from a reactor are highly radioactive and give off heat. They must be handled remotely, kept in cooling ponds at first, and then stored securely as nuclear waste. Radioactive waste is a major disadvantage of nuclear power.