The material cause refers to the physical cause of the object. It occurs because of the parts or materials that have made it. Take the example of a book. You'd need paper, a printer to print words and a cover to make a book live up to its purpose.
The formal cause refers to the pattern by which something is made. With the book example, it's how the different materials are supposed to fit together. It is a type of mental image which lets you tell a book from any other object.
The third type is the efficient cause. This is what other things caused the item to exist. A book may be crafted by hand or be put together by machines. Aristotle would say that the knowledge, rather than the crafting of the book is the real efficient cause.
The fourth cause is the final cause and this shows the purpose of the thing that was made. Aristotle said that the final cause is the end (telos), that for the sake of which a thing is done. The final cause of a book is to be read, this is the desired end and it is what all the other causes lead to.
Potentiality and Actuality
Potentiality is when something contains the ingredients to become something else e.g. a kitten has the potentiality to turn into a cat.
Actuality is achieved when something fulfils its potential and becomes something else e.g. a cat has fulfilled its potential as it continues to be a cat for the rest of its life, it can't change into anything else.