Pattern welded steel got the name "Damascus" because that city was a major trade center during the Crusades, and European knights first ran across the steel there.
To over simplify a bit, steel is iron with carbon added. Iron carbide is a whole lot harder than iron. Using primitive methods, it is close to impossible to melt iron, which makes refining steel difficult. But, if you heat up a sheet of impure iron in a forge, fold it in half, and pound it flat, you will knock out some slag, and some carbon from the forge will find its way into the iron. Do that enough, and the iron becomes fairly pure, and the addition of carbon changes the iron to steel. Since the folding process welds two layers of steel together, the effect is something like plywood, which is stronger than plain wood. Theoretically, the number of layers doubles with each fold, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Some people might claim that ten folds will give you over a thousand layers, but in practice it doesn't work out that way.
if you use two different kinds of steel, one will be more acid resistant than the other. So, if you do an acid etch, a pattern will emerge. There is no advantage to etching, other than cosmetic. I am not sure if it is still available, but the chemical Radio Shack used to sell to etch circuit boards used to be reasonably good.
Now, of course, the people who make pattern welded steel start out with refined steel instead of, say, meteoric iron. The product is pretty, but I do not believe it has many engineering advantages over a good alloy steel.