From /r/knives:

..."Real" damascus steel is an ancient type of steel which originated in Sri Lanka, IIRC. It was leagues better than the steel available at the time, which wasn't that much better than iron. Damascus steel was more homogeneous, meaning the carbon in the blade wasn't in large chunks and was evenly distributed through the steel. We don't know the exact recipe or process that was used, but we can make similar stuff.

It was commonly forge welded (or pattern welded), which means that billets of steel were stacked together, heated up to forging temperatures, fused together by being hammered, flattened out, folded on itself, and forge welded again. This further increased the homogeneity of the steel and improved its grain structure.

With modern metallurgy, neither of the above are necessary to make good steel. However, sometimes people make pattern welded steel out of two different steels, then dip it in acid when the blade is done. The acid eats away at the steel, but it eats away at the different steels at different paces. When the blade is cleaned off, the difference in the two steels stands out prominently, in the characteristic "damascus steel" pattern. This isn't really damascus steel, nor is it at all necessary to do, but it's pretty and gets called "damascus" anyway.

From /r/AskHistorians:

...There's two types of steel called Damascus steel, you can't see a difference with your naked eye.

The first (pattern welding) is a folded steel, with two initial layers of high and low carbon steel. This is not actually remarkable other than its appearance compared to other steels of the time.

The second, which the legends come from (its not up to that level, but the stuff is unique), is a crucible steel. With and low carbon steel that contain one of vanadium, molybdenum or a third I forget. Very very small amounts of these elements are needed, around 100 parts per million, the technique was likely lost because the iron mine the crucible version was being made of was shut down, and it was actually budget concerns that led the metallurgist who discovered this to use an ore with appropriate impurities, he knew they were in the wootz damascus steel but thought them too trace to be significant.