The proposed process is to use the x-ray band bremsstrahlung photons from a electron accelerator (see also advanced light source) to initiate photo-disentigration reactions in long lived radioisotopes with the goal of generating either stable daughters or short-lived daughters that will decay to stability in a reasonable amount of time.
Here's a randomly chosen photo-disentigration paper for Am-241 which is long enough lived to be hard to store, but active enough to be dangerous.
The idea is not new (I recall seeing a colloquium talk on the subject from a Los Alamos scientist in the mid 1990s and his pitch was "we may be getting there"), but it is a very difficult technology and the need for a particle accelerator has long made it a power hungry one as well. Recent improvements in accelerator design have improved the available beam power and the efficiency with which these beams can be produced.
These kinds of processes are of active interest to the US Department of Energy which is funding them as part of it's activities on "the intensity frontier". Quote from the last section of the linked Fermilab blurb:
In addition to its broad program in fundamental science, Project X could support R&D towards the destruction of spent fuel from conventional nuclear reactors, and the development of accelerator-driven subcritical systems for safe and abundant nuclear energy production.
The issue of high radio-toxicity and the long lifetime of conventional spent nuclear fuel is a global challenge. Accelerator-driven systems can be used to transmute spent nuclear fuel, significantly reducing the lifetime and toxicity of nuclear waste.