Aristotle agrees with Plato on several things. For one, he thinks that there is a difference between appearance and reality. He also thinks we have a soul, and that knowing our soul is the route to knowing reality, at least for ourselves.
But there are important differences.
1. Plato thought that our souls were eternal and lived with the forms before we were born. Aristotle thought that our souls died when our bodies died. Souls are the highest aspect of what we are.
2. Everything is made up of two parts: matter and form. The form is like a soul. In this sense, everything has a soul. Our souls are of a particular kind. We are the only beings with rational souls.
3. Getting to know yourself, then, is the same as getting to know anything. First, you figure out what kind of a thing it is, that is, what its defining feature is. Then, you examine that feature, to determine what follows from positing that it exists.
Example: The defining feature of the heavens is that everything goes in circles, as opposed to the earth, where things go in straight lines. To know about the heavens, then, you deduce what you can know based on the fact that things go in circles. What do circles suggest?
- Everything up there is eternal
- Everything up there is perfect
- There was no beginning
- What is up there is "simple" (cannot be corrupted)
And what about the earth?
- Things have beginnings and endings
- Things are not perfect, since they break down
- Things are not simple, but composite
Now, our souls are "of the earth" - they are corruptible, they begin and end. However, there is a certain sense of perfection, in that they strive to be better than they are. They strive to be like God. That is our highest nature.
Who are we, then? We are a combination of matter (bodies) and form (soul), which is rational (that's what kind of soul we have), and therefore organized in a particular way (i.e., politically), and striving for pure reason, the highest faculty of the soul.
There's a lot more, but that's a start.