The process of transmutation changes the nuclei from one isotope to another one.
The deposition of nuclear waste from light water reactors -- just after reprocessing -- is complicated, dangerous and not foreseeable because some isotopes decay within hundreds of thousends of years. There is now known possibility to store theses wastes during such time scales.
Transmutation can convert long living isotopes like plutonium or strontium into short lived isotopes which decay in a range of hours. The radiation doses per time unit are much higher but will fall below dangerous levels within foreseeable time scales -- within some weeks ore months.
Transmutation can be invoked by bombarding nuclear waste with high energy protons emitted from a particle acceleratur. The treated waste will be separated into long living isotopes and the short living ones. Long living isotopes will be processed until they are converted. Short living isotopes were stored until their radiation levels are below a threshold which allows to deposit them in a nuclear waste repository.
Such a treatment has to be calculated into the whole process of nuclear energy production. The energy efficiency of the accelerator, conversion efficiency and the separation efficiency have to be high enough to result in a positive energy bilance.
Transmutation is proposed as nuclear waste treatment but never experimentally confirmed as solution to the nuclear waste problem. Destroying nuclear waste is a much better solution compared to the direct storage of used fuel rods or the storage of processed nuclear waste because it can be handeld by human time scales and avoids the problem of the release of dangerous isotopes into the biosphere.