In Greek, xeros means "dry," and graphein means "to write." Put them together and you get the English word "xerography," which means "the process of making dry written copies of things, without having to use wet ink."
This process was invented in 1938 by a scientist named Chester Carlson. By 1952, Carlson's company, The Haloid Company, had used xerography to create a machine that they named the Xerox.
Over time, we started using the word "Xerox" so much that we stopped capitalizing it and started using it like any other verb. Like this: "Can you xerox these papers for me?" "Hang on, I've got to xerox this drawing so we can all look at it up close."
In other words, to xerox something is to make an exact photocopy of it, using a machine. "Xerox" means the same thing as "photocopy," but "xerox" is faster to say, and more fun to say!
These days, as we use our digital devices more and more, and as we try to reduce how much paper we use, we try not to xerox things unnecessarily. But xeroxing is still useful, and still fun!