Damascus Steel is a broad category of metallurgical techniques used to make higher technology knives and sword blades in the 12th through 18th centuries. Prior to the Bessemer process which allows steel to be made in large quantities with exact control over the amount of carbon in the mix, steel was made in an artisanal method – it was made in small batches, and making a batch large enough to make a sword was a technical challenge.
Steel is iron with carbon impurities; the best time to mix in the carbon impurities is when the steel is hot. The archetypal image of a blacksmith striking sparks from a red hot steel blade that we see in movies and popular culture stems from needing to distribute the carbon (from coke or charcoal) through the blade. You'd hammer the steel while it's glowing hot, turn the blade over, hammer it again, and reheat. The aim of doing this was to make sure that the carbon granules were broken to the right size in the alloy. (Modern steel making allows much greater precision than merely hammering the nodules out). The more carbon there is in the steel, the harder it is, and the more rigid the steel is.
Damascus steel, in spite of the mythologies that have built up around it, was simply a technique of taking high carbon steel ingots (usually "wootz" steel imported from India), hammering or drawing them flat, and then putting a layer of charcoal over them, then a layer of higher nickel alloy steel over it (nickel keeps steel flexible), then hammering them together, often times trying to fold the steel back so that there's a pattern of high carbon steel (providing rigidity) and softer nickel steel (maintaining flexibility and the softness needed to sharpen the weapon with period tools).
Damascus steel shows a distinctive pattern – the high carbon steel is darker than the nickel steel, and there's a pattern of cells that can look almost like snakeskin or running water through the blade, as the hot blade is quenches in pickling brine. (This brine will tarnish the high carbon steel before the nickel steel). Similar patterns can be found in pattern-welded steel swords from Northern Europe and the "folded steel" swords of the Japanese, both of which have been mythologized (as has Damascus steel) into weapons that can cut rock, bodies and machine gun barrels.
Damascus steel fell out of fashion for two reasons. The first is that it's incredibly labor intensive to make, and the second was that with the Bessemer process, modern steelmaking allowed for comparable steels at a fraction of the cost. Indeed, the leaf springs in a typical automobile or light truck can be ground down to make better swords than ever existed in antiquity in terms of quality and ability to hold an edge.
