Natural rubber has been used for centuries because there are so many uses for it. One problem with rubber is that it is soft and can break down rather quickly during use. That means that it needs to be treated in some way so that it will last longer. For many centuries, the way that rubber was treated so that it wouldn't break down as quickly or easily was to cure it. However, in the 1800s, another treatment was developed called vulcanization.
The vulcanization process was discovered by a name that may be familiar to you, a man named Robert Goodyear. He was looking for a faster and easier way to make sure that natural rubber was treated to make it more durable and longer lasting. Vulcanization is named what it is because it is named after Vulcan, who is the Roman god of fire, and incidentally, the same person that volcanoes are named after. The reason that Vulcan's name was used is that the original process included high heat. However, as the vulcanization process was refined and technology advanced, different kinds of processes were used.
The goal of vulcanization is to make the rubber harder, less viscous, and keep it from breaking down or deforming. The way that it happens is that the polymer chains inside the rubber are manipulated by the various processes and then are cross-linked, or connected together. Without that, the polymer chains are individually placed and can move around. Imagine it like several lines of beaded strings laying side by side. Without being vulcanized, all of those strings can move around by themselves, slipping side to side or up and down. The vulcanization process makes it so that they are linked together. Instead of being all one direction laying side by side, the process will make it so that the strings will look more like a mat. There will be some strings that lay vertically while others lay horizontally, linking everything together into one solid mass. Those strings can't move independently anymore. That hardens up the rubber, gets rid of the viscosity and stickiness, and makes it more durable. The process is accomplished by using various chemicals and heat to rearrange those polymer strings. Those chemicals can include things like sulfur and metallic oxides.
When it comes to your tires, the soles of your shoes, and even hockey pucks, vulcanization is a necessary process so that they will last as long as possible.