Folded steel is different from pattern-welded steel. The term refers to a tradition which I only know to have existed in Japan.
A smith would take the single piece of steel he planned to use to make the sword or knife from, and hammer it out flat and wide. Then, while it was still hot and soft, he would fold it over itself, which made it thicker, not as spread out, and distinctly two-layered.
Then he'd grab the hammer again, flatten it out again, and fold it again, and get a four-layered piece of steel. The next step gives him an 8-layered piece, then 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, and 32768, if he goes up to 15 folds, which is the record.
Each time the steel is tortured like this again, it gets a bit more pure because nasty stuff other than steel comes out in the process. So does some iron and carbon, the essence of steel, so the billet also loses some mass each time through the cycle, but that's OK if you compensate by starting with more steel than you intend to have in the final product.
The process serves a few purposes. It removes impurities, which amount to disruptions of atomic structure, which would mean weakness if they were left there. It also tends to distribute whatever atoms are in there (especially carbon) fairly more evenly through out the piece, "homogenizing" it. A piece of steel that's not the same formula throughout will also have structural problems that make it weak. And, finally, the layering, once you get well into the thousands, tends to promote the formation of crystalline structure in the atoms' arrangement, which is also good for strength.
You increase the benefits significantly up to around 10 folds. After that, it doesn't makes things worse or better, you're just working a lot and making the billet a little bit smaller and lighter. This dwindling-mass factor could be used to advantage; it was common for a smith to use the last few folds just to control the size of a billet in which the metallurgical standards were already met.
It was a way of dealing with impure iron ore (acutally an iron-rich volcanic sand, I think) called "tamahagane" with the best technology and technique that was available. A modern steelmill can produce huge amounts of steel, in various shapes and sizes, in almost any precisely-measured formula, which outdoes folded tamahagane in every way that folding was meant to improve, at a cost that's microscopic by comparison. But the ancient Japanese smiths didn't have modern steelmills or even our understanding of the chemistry and atomic physics at work, so they came up with the neatest trick they could. One guy I know on swordforum.com, who often has to talk some reality into people who think there's something magical and perfect about old Japanese swords, refers to their steel as "modern 1060 with crud between the layers".
Folding is still done by some smiths, for a couple of reasons. One is a matter of tradition, which tends to be a much more driving force in Japanese culture than in ours and lends an air of history to even a modern-made blade. Another reason is art; the blade of a Japanese sword or knife shows off some interesting subtleties within the metal which I can't quite describe, and a lot of this depends on the impurites and their not-quite-even distribution, which folding leaves and a modern piece of 10xy series steel doesn't have. Smiths at swordforum.com periodically discuss the challenges of getting a Japanese-style sword to look the way they want it to using modern steels such as 1075, W1, L6, etc.; modern, scientifically conditioned stuff can sometimes be just a bit too perfect to have quite the personality that an artistic smith wants.
