Aristotle's doctrine of substances divides objects in the physical world into two major components:
matter and
form. Matter is present in all
physical objects, can change into anything, and is what allows substances to change. Forms are what determine the
properties of objects and how they interact, and are the components of objects that are
knowable. There are some substances that exist as form without matter, but these are, by definition,
insensible,
unchanging, and
eternal. Describing such things requires a bit more detail on Aristotle's doctrine, so we start first by describing more completely what Aristotle means by defining things as substances.
Aristotle defines a substance first as that which is the subject of predication; that is, the topic of a sentence. When we say that the robber robbed the bank, the robber is the subject of predication, and is thus a substance. A substance is also that which persists through change - the robber is still the robber before and after the theft. So generally speaking, individual objects are substances. All physical objects are composite substances, containing both matter and form. Their matter allows them to change, and their form grants them their properties.
Matter also allows for things to be many in number. A form is a singularity. There is only one form of blueness, and yet there are many blue objects, such as bluebirds, blue cereal boxes, blue books and blue rocks. Each blue object is a bit of matter, with the form of blueness inside of it. Each human is a bit of matter with the form of rational animality inside of it. "How can the single form of blueness be in all these places at once?" some might ask. Aristotle cleverly puts this in his definition of forms: forms are universals, able to exist in different objects in different places at the same time. Objects can contain many, many forms, and in fact must, because otherwise huge numbers of things would be indistinguishable. So matter allows for plurality amongst the things of the world, while forms allow for individuality between these things.
I have said that matter allows things to go through change. A robber puts on a fake nose and glasses as a disguise, and changes his appearance, but he is still the same object. But does this apply to all kinds of changes? Suppose the robber is shot by a police officer. There has been a change in the robber… his heart no longer pumps blood to his organs, he no longer breathes, and his brain no longer operates. Aristotle will tell us that there has been such a change that he is no longer the same object. He has lost a substantial form, the form of being a rational animal, because he no longer thinks. A substantial form, for Aristotle, is a form which defines the kind of thing that a substance is. The essence of the substance, if you will. When that form is altered, the object ceases to be what it was, by definition.
An accidental form, by contrast, is any form that is not a substantial form, and can be altered without an end coming to the object that it is in. If the robber has his hand shot off, he is still a rational animal. If he dyes his hair or learns how to fly, he is still a human being. Again, matter allows for changes like these to occur, because matter can become anything.
Formed matter is matter that contains forms, and thus has sensible, describable properties. All physical objects are formed matter. Unformed matter has no properties, and so beyond being insensible, simply does not exist. Form that is not inside matter does exist - the human mind is one example of this. When a human thinks, according to Aristotle, his mind takes on a certain number of the forms of the thing he is thinking about. If I think about a black cat, the forms of blackness, catness, hairyness, and several others appear in my mind, merging into the idea of a cat. The mind cannot consist of matter, because if it did, when the form of a cat came into my mind, it would combine to create a physical cat inside my head. Form + matter = substance.