Today, alum, as a chemical, is barely good enough to rub on your armpits as deodorant. During the 1400s, it became so crucial to the economy that the Papacy formed cartels to protect its monopoly on the trade.
Alum is known more specifically as potassium alum KAl(SO4)2, a combination of potassium, aluminium, sulphur, and oxygen. These crystals can firm up the walls of cells. When you bite down on a pickle that's still crunchy, even though it's been in a jar full of brine for months, or a maraschino cherry that's firm, despite having been suspended in syrup, you're probably eating a little alum.
Alum is also a natural bactericide, so it's one of the main ingredients in deodorants. Unfortunately, it doesn't limit its damage to bacteria. According to the FDA it's safe to consume small quantities of alum -- the page on potassium alum sulfate points out that between trace elements and aluminium cooking pans there's aluminium in most foods -- but many people avoid foods or deodorants with alum in them.
About five hundred years ago, alum was mainly used as a mordant for dyes. Mordants form compounds with the dyes, which then attach to the cloth or tissue being dyed. They're the reason why dipping a bit of cloth in soapy water doesn't wash the dye right off of it.
Textiles were one of the first industries to span multiple countries. Wool could be made in one country, spun and woven in another, and made into clothing in a third. Many nations were dependent on the textile trade, which meant alum was incredibly valuable. Fortunately, it was plentiful. Unfortunately, it was most plentiful in the eastern Mediterranean, which was controlled by the Turks. As this was during the stretch of time when Christians were trying to expand into Muslim-controlled territory and Muslims were trying to expand into Christian-controlled territory, Christian Europeans buying alum would essentially be enriching the enemy.
In 1462, miners at a Papal-controlled mine near Rome found large deposits of alum. Suddenly, no one had to make the choice between fighting new crusades and keeping the economy going. There was enough alum for everyone, and the Pope himself was selling it. As soon as the trade was established, cloth makers discovered that their troubles weren't over. The Pope needed money as much as anyone else, and the 15th century Popes had not only control over alum, but a religious reason to condemn anyone who wasn't buying what they were selling.
Heard of the Medici family? They gained part of their wealth because, for a time, they were granted a monopoly on Italian-produced alum. Everyone involved in the trade had reason to keep the price high, so soon the Papacy formed cartels of miners, refiners, bankers, and traders who cooperated so that no one really had a choice about what price they wanted to pay for alum. If they wanted a choice, and thought about trading for Turkish alum, they could enjoy their excommunication.
Eventually, Pope Julius II pushed the price too high. Entire economies broke down because no one could afford to pay the Pope's price for alum. Something had to change, and soon it did. Kings, emperors, and bankers quietly came up with a scheme to import, "launder," and sell foreign alum. At least one historian makes a case that this illegal chemical trade is partially responsible for England's rise as a nation. King Henry VII allowed foreign ships to come in, carrying Turkish alum. This gave it an air of plausible deniability, and exported the alum to cloth-dying countries. King Henry VII took a fat cut of the profits and filled the royal treasury sufficiently to build up the nation.
What a difference a crystal makes.
[Source: The Winter King, by Thomas Penn]