Ordinarily nuclei have to be moving very fast to have enough energy to actually collide and fuse. That's because they're all positively charged, so they repel each other electrically. Getting that much enregy in the nuclei either requires getting them very hot or systematically accelerating them toward each other.
The idea behind cold fusion is that if there were some way of reducing the repulsion, then the nuclei wouldn't need so much energy to fuse. One way to do that would be to have a heavy negative particle that would bind tightly to a positive proton, cancelling its electrical field except at very short distances. That actually is doable, but only with unstable negative particles that require a lot of energy to produce, and then rapidly disappear.
The initial, incorrect, experimental reports of cold fusion were unclear about how it was supposed to work. Then some theories were made up about how the electrons were supposed to play the role of heavy negative particles, even though they aren't heavy and don't bind very closely to the nuclei. These theories were also wrong. Most of the reputable scientific community has abandoned this area, although there are a few die-hards.
(published on 12/16/2007)