The one thing absolutely necessary to leather working is obviously leather
There are many different kinds of leather available to purchase, from veg-tan (more detail on what exactly this is in a sec...) to exotics like stingrays. From buffalo to kangaroo, you can buy it and make things out of it.
By far, the most common type of leather is called veg-tan. The "tan" part of the word "veg-tan" refers to tanning, which is the process by which the skin of an animal (after removal from the body) is treated so that it will not decompose and biodegrade (rot away and stink to high heaven!) therefore becoming a durable material that can be used to make things from. In the "olden days" I believe they used brains, urine and salt to complete that process, but now use chemicals that are vegetable based, which is where the "veg" in "veg-tan" comes from. The veg-tan that is available for purchase from Tandy Leather Factory and other suppliers is generally from cows. There are 2 sides (like a coin) a skin or finished side, and the flesh (suede) side where it was previously attached to the animal.
It is in an unfinished state, meaning undyed, and generally quite stiff, which is why you'll find it either laid out flat or rolled when you go looking for it in a retail setting. You cannot fold veg-tan for storage because with this unfinished state, it would permanently crease.
You can do many things with veg-tan, like dye it to a color of your preference, stamp it (using a metal implement struck with a mallet to impress a permanent image on the leather) sew it, brand it (burn an image or design into it) and tool it. Tooling is a multi-step process of cutting and stamping custom designs into veg-tan that uses both positive and negative space to create the image. It is a VERY hard thing to master, because one misstep with a stamp and a mallet, and you can permanently flaw your design. However, tooling in the way of the masters of this craft, is not necessary to creating a leather item. Many items use no tooling or stamping at all. But if they do, they started as veg-tanned leather.
There will be many different qualities among veg-tanned leather. The lowest (and therefore least expensive) will be thin and will also have marks on the finished side, where the animal may have been branded or have scars where the animal may have sustained an injury at some point in it's life. There may also be scars from bug bites that will be visible, or have holes in it where it was cut away from the animal. The highest quality hides (and mot expensive) will be unmarked to provide the most usable surface with the least amount of flaws.