Philosophers sometimes say there are basically two kinds of philosophy — speculative philosophy and analytic philosophy. Speculative philosophy is, as you might guess, concerned with speculation. It is characterized by concern for the “big problems” — e.g., meaning of life, why is there something rather than nothing. It features “broad brush strokes of thought.” Speculative philosophers tend not to express their views in argument form with premises and conclusions, and to use poetic and vague language freely.
Analytic philosophy is sometimes called critical philosophy. Analytic philosophers tend to tackle problems more modestly and systematically, and build large systems up from numerous well-constructed components. They tend to be philosophically economical — they don’t buy concepts they don't absolutely need, in accordance with a principle called “Ockham’s Razor.” They look for provability. They are suspicious of poetic language.
Plato, Aristotle's teacher, tends to be a speculative thinker. Aristotle is the first great analytic philosopher.
Aristotle (384-322 B.C.) was a student of Plato. Aristotle spent 20 years in Plato's Academy until Plato's death. Then he left, tutored Alexander the Great for a few years, and eventually started his own school (the Lyceum) in Athens.
For sheer breadth of work, Aristotle stands out. Most other philosophers are famous for one or two areas of philosophy, e.g., Aquinas for philosophy of religion, Descartes for metaphysics, J. S. Mill and Hobbes for political philosophy. Aristotle, by contrast, had his hands in everything.
To get an idea of the flavor of Aristotle's philosophy, it's instructive to contrast it to Plato. Some people say Plato is a poet, while Aristotle is an engineer; or Plato is a dreamer, while Aristotle is a practical man; or Plato is a rationalist (stressing the power of reason unaided by experience to grasp substantial truths about the world), while Aristotle is an empiricist (stressing knowledge from experience).
Let’s contrast the views of Plato and Aristotle on three key questions:
Regarding ethics, Plato says virtue is sufficient for happiness, while Aristotle says virtue is necessary for happiness.
Regarding psychology, Plato sees the body as a “prison” for the soul. For Plato, the life of the soul in the body is contrary to its nature. So Plato is a dualist with respect to this question. Body and soul are radically different kinds of things, capable of existing separately, and it's assumed that the soul is superior to the body.
For Aristotle, body and soul are different kinds of things, because one, the body, is matter, and the other, the soul, is form. But this is not to say the body is a prison, or that the soul is “better” than the body. Everything in the universe is composed of matter and form, so it's not surprising that persons are too. Form is simply the way matter is put together. Dogs are put together in a doggy way; that’s what makes them dogs. Rocks are put together in a rock-ish way; that’s why they’re rocks. Persons have a special mode of organization, too; that’s their Form. In fact, nothing can exist in our world which is NOT both matter and form. Everything is something; in other words, everything that is in our world is matter organized in a certain way. Take away the organization and the thing isn’t anything any more; it ceases to be, since for Aristotle, to be is to be something, and to be something is to have a certain form. So for Aristotle, the concept of soul without body or body without soul is incoherent. We should note that Aristotle himself was not happy with this answer and argued that souls might be able to exist without bodies; but he never concludes they do.
You can think of the difference between Plato and Aristotle on this subject in sci-fi terms. When people talk about souls inhabiting different bodies, like in Steve Martin's movie All of Me, they are being Platonists. Aristotle would not understand this at all.
Regarding Forms, then, Plato explained how things are the way they are (like the question “Why is the frying pan a frying pan and not something else?”) using poetic and vague language. He talks about things “imitating,” or “participating in,” or “reproducing” Forms, which are like ideal models of things, e.g. the frying pan imitates the ideal frying pan. Plato talks as though the Forms actually exist, though it's not clear “where” or how.
Aristotle is more philosophically economical than Plato; he tends to get rid of concepts he thinks are unnecessary, and he thinks the notion of Forms existing apart from things (transcendently) is superfluous. Aristotle moves the forms right into the things; he makes them immanent. The frying pan is a frying pan because it has a material part (the metal) and a form (“frying pan-ness”). Frying pan-ness is not “out there” somewhere.
To sum up, you can see Aristotle as someone who finds the world terribly interesting just as it is. His focus is always on explaining things in a way consistent with experience, without introducing extra fantastical notions that can't be proved. I think of Aristotle as a kid from the sticks who entered Plato's Academy as an outsider, and always remained an outsider, because he just couldn't shake that empirical, practical bent. He's rather like the Lt. Columbo of Ancient Greek philosophy. Aristotle has the engineer's temperament; he likes to get things clear and solve problems. Plato's vague, poetic language in metaphysics and ethics didn't inspire Aristotle; it made him uncomfortable. And this made Aristotle produce one of the great systems of Western philosophy.