by Motoyasu

A vastly simplified description is: you get a small ceramic pot (the crucible), and load it with bits of iron ore and charcoal and whatever other "secret ingredients" you want, and put it into a furnace and blast for many hours until the small bit of iron in the crucible melts and combines with the carbon to form steel and all the impurities float to the surface. You skim off the slag, and are left with a small amount of fairly pure steel.

Before this process was discovered, what smiths did was gather up unprocessed iron ore, and forge together into a billet much like the Japanese did with their tamahagane, then bake the billet for several days in a bed of coal so that a bit of carbon would go into the surface and become steel (case steel), the billet would have been folded, and the baking process repeated many times to get the carbon up to an appropriate level, and then it would be forged into a sword. The Europeans in general didn't fold nearly as many times as the Japanese, so there were many impurities left in the resulting steel.

The crucible process that the Spanish first obtained from the Moors allowed them to make the smelted steel, which would have been of vastly superior quality to the other materials of the time, and so, Spain, in particular, Toledo, got its reputation for superior swords. Of course, the technology quickly spread, and before long, everyone had access to smelting technology.

The difference between the early European crucible steel and Damascus is partly in the composition (Wootz Damascus is of extremely high carbon content - well over 2%, and it also has a significant silicon content), and partly in the processing - instead of forging the billet at high heat, a Damascus billet was worked at relatively low heat and hammered over and over again to break up the steel grains - it takes on a property known as "superplasticitity" which allows it to be forged at low temperatures despite its incredibly high carbon content. Also, because of the high carbon content, a lot of hard carbides form in the steel and precipitate out, and these carbides are visible in the surface of the finished blade and form the "watering" that true Wootz Damascus is famous for.

Of course, the actual process is much more complex than it sounds, if you're interested in it, see the article in the Scientific American.