It is called cold fusion, because it is said to occur at or near room temperature, as compared to conventional nuclear fusion, which requires a very hot (100 million degrees) plasma.
The most common experiments involve a metal electrode (usually palladium or titanium) which has been specially treated so that it is saturated with dueterium and placed in an electrolytic heavy water solution. The experimenters saw extra heat coming from this system which was not readily explained by the electrolytic reaction itself. Some experiments also saw some fusion products (helium and tritium), but basically no nuetrons coming from the experimental cells.
There are still a few people trying to do cold fusion, for example: http://www.mv.com/ipusers/zeropoint/IEHTML/faq.html
Bob Park gives a decent account of cold fusion and its history which represents the perspective of the mainstream scientific community. Robert L. Park: Voodoo Science. The Road from Foolishness to Fraud. Oxford University Press, New York, 2000.