The short version, for those of you too lazy to read (and you really should), is this: microscopic synthetic rods called carbon nanotubules are inserted into cancer cells, and exposed to near-infra red light from a laser. This makes them heat up, killing the cell, while cells without rods are left unscathed. The real trick is getting these nanotubes to the cancer cells and not healthy ones, and researchers did this by taking advantage of the fact that, unlike normal cells, the surface of cancer cells is covered with receptors for a vitamin known as folate. They coated the nanotubules with folate molecules, making it easy for them to pass into cancer cells, but unable to bind with their healthy cousins.
This could be the first real breakthrough in fighting cancer that we've seen in forever. If it gets the results it looks like it could get, well, I don't want to say "this could be the end of cancer", but it could damn sure take the sting out of it.