Scribes carved the first writing on wet clay tablets, but soon after that, about 3000 BC, the Egyptians invented papyrus, and by about 500 BC most people in West Asia and the Mediterranean used papyrus for writing. They couldn't make papyrus, though, because papyrus reeds wouldn't grow in their countries, and they had to buy it from the Egyptians. Papyrus was very expensive. People used to write on broken pieces of pottery and wood and wax tablets because it was cheaper.
Then about 150 BC the Pharaoh Ptolemy V of Egypt refused to sell any more papyrus to King Eumenes of Pergamon (in West Asia) because Ptolemy was afraid that Eumenes' library was going to get to be as good as his own. So Eumenes began to make his books out of parchment instead.
Parchment is made from animal skins. Usually people used the skins of sheep or cows, because those animals were pretty common in West Asia and Europe. You took the skin and scraped off all the hair from the outside and all the fat from the inside. Then you soaked the skin in water with chalk or flour and salt added to give it a good smooth surface to write on. And finally you soaked the skin in tannin made from oak-gall, to preserve it (like pickling something). Our word parchment comes from Eumenes' kingdom, Pergamom.
Parchment was even more expensive than papyrus, and so papyrus continued to get a lot of use until the fall of the Western Roman Empire about 400 AD. After the fall of Rome, Europeans didn't trade much with Egypt anymore, and had a very hard time getting papyrus. So more and more they used parchment, or they didn't write at all, because parchment was so expensive.
By about 800 AD, even the Egyptians weren't using papyrus anymore, because they had learned about the Chinese invention of paper, which was much cheaper. All over the Islamic Empire, people were using paper- and writing a lot! But in Europe people were still using parchment, and writing as little as possible.
In the 1200s, though, Europeans conquered some Islamic territory in Spain, and captured a paper mill. They learned how to make paper, and within two hundred years nobody was really using parchment anymore except for special things like diplomas and letters between kings.