One of the nicest things about Aristotle is the way he takes time to explain the definitions of the words and concepts with which he deals very clearly and to carefully clarify the relationship between the various terms of the definitions. I have to go over his definitions of soul for my Philosophy of Man final, so I figured I'd try to schematize and post them, for want of anything better to say.
The first full definition of soul that Aristotle gives in De Anima II,1 calls it “a substance in the sense of the form of a natural body having life potentially within it”. Aristotle here understands substance in the second sense that he presents, as the actuality of a body, or as basically identical with form. The form is “that precisely in virtue of which a thing is called a this” - it gives a body its identity as what it is, actualizing its matter, which at the most basic level is purely potential. The soul is the actuality of a body having life potentially within it in the sense of the “first grade of actuality”: that is to say, it is the principle which organizes the matter in such a way that a certain activity is proper to it. Aristotle is thus presenting a distinction between two types of actuality: whereas the second, most complete, level of actuality involves the active exercise of the function proper to a body's essence, first actuality simply involves possession of and readiness to use this function. It makes sense that the soul would be the first actuality rather than second, because Aristotle would by no means want to say that simply because a person were, for instance, not actively thinking, he would somehow not have a form at that point – a sleeping person has just as much of a soul as a waking one; the person who is awake is merely pushing the first actuality of possession of knowledge in his soul into second actuality by thinking it.
Aristotle follows up this definition with a second one that ties in a few more elements of his understanding of the soul. It is, he says, “a substance in the sense which corresponds to the definitive formula of a thing's essence”. It is the “essential whatness” of a body which has life potentially within it. This formulation emphasizes the relation of actuality to essence: the characteristic act of a body makes that body what it is, just as the activity of cutting wood makes an ax an ax. Whatever function is proper and essential to an object's way of being is its actuality and thus its essence.