What most call "Damascus Steel" is really "Pattern-welded Steel", and that is what Kile described. In the past, it was used to make blades that had the edge keeping ability of a harder steel (higher carbon) and the ductility of a lower carbon steel or iron. As an added benefit, the repeated heating, folding and hammering required to make such a blade tended to work carbon more evenly throughout the blade and to work undesirable elements out of it. This form of blade work was used extensively up to about the 11th Century CE in the Europe, when they began to develop the technology to make homogeneous steels in quantities large enough to make whole sword blades. At this point, pattern-welding began to fall out of use and became, for most purposes, a forgotten art until smiths such as Jim Moran revived it in the mid-20th Century. Now it is used primarily as an art form.
What I said about Europe does not apply to the Far East, as Japan continued to use pattern-welding up into the19th Century and beyond, and others may have done the same.
"Damascus Steel" is correctly applied to a steel made by the Wootz process of baking the ores and the other elements that you wish to have in the final steel in a closed container. The baking takes place at extreme temperatures, so that the contents of the retort melt and blend together into one alloy. You can tell real "Damascus" from "Pattern-welded" steels by the blade designs. While "Pattern-welded" blades have the characteristic wavy lines running through them where you can see the many layers built up by the folding and refolding, "Damascus" has the lines plus the matrix of the stell itself. The swordsmith or knifesmith takes the cakes of Wootz steel from the retorts and pounds them flat and into the basic shape that he wants before forge welding them together into one blade. A true Damascus blade is a thing of beauty to behold. A friend of mine has one that was authenticated by the Smithsonian as being Middle Eastern from the 8th Century CE. The blade is simlply gorgeous, light, quick, alive in your hand, and he demonstrated its ability by flexing it so that the tip of the blade touched the pommel of sword's hilt and then letting it slowly go back to straight again. This was on a 1200 year old blade!