High-level waste (HLW) is highly radioactive material arising from nuclear fission. It can be what is left over from reprocessing used fuel, though some countries regard spent fuel itself as HLW. It requires very careful handling, storage and disposal.
Intermediate-level waste (ILW) comprises a range of materials from reprocessing and decommissioning. It is sufficiently radioactive to require shielding and is disposed of in engineered facilities underground.
Low-level waste (LLW) is mildly radioactive material usually disposed of by incineration and burial.