What is metaphysics?

Metaphysics, according to the Aristotelian Thomistic meaning, is several things:

1. The science of being as being
2. The "First Philosophy" (first in the sense of "ultimate", but last in the order of our learning)
3. "Beyond physics"
4. The study of "one"

Modern philosophy, however, gives a much broader definition of metaphysics: "The branch of philosophy that deals with the first principles of things or reality, including questions about being, substance, time and space, causation, change, and identity (which are presupposed in the special sciences but do not belong to any one of them); theoretical philosophy as the ultimate science of being and knowing." (OED).

For a Thomist, "questions about" "time and space, causation, [and] change" are parts of natural philosophy, not metaphysics.

St. Thomas says of "metaphysics":

1. "one" which is convertible with being is a metaphysical entity and does not depend on matter in its being. (ST I q. 11 a. 3 ad 2)
2. …the highest of [the sciences], viz. metaphysics… (ST I q. 1 a. 8 c.)
3. …acquired knowledge about Divine things, for instance, the science of metaphysics… (ST II-II q. 9 a. 2 arg. 2)
4. …metaphysics, which treats of being or substance… (Post. Anal. I lec. 41 b)
5. Metaphysics at once studies being in general and first being, which is separated from first matter. (De generatione proem.)
6. It is called metaphysics inasmuch as it considers being and the attributes which naturally accompany being (for things which transcend the physical order are discovered by the process of analysis, as the more common are discovered after the less common). (In Meta. proem.)
7. metaphysics, which deals with divine things, is the last part of philosophy to be learned (CG I a. 4)

St. Thomas says of "physics" (natural philosophy, natural science, or philosophy of nature):

1. …physics, which treats of mobile body [i.e., changeable bodies]. (Post. Anal. I lec. 41 b)

Basically, if there are no such things as immaterial beings, physics would be the ultimate or first science (In Meta.VI lec. 1 [1170]):

if there is no substance other than those which exist in the way that natural substances do, with which the philosophy of nature deals, the philosophy of nature will be the first science. But if there is some immobile substance, this will be prior to natural substance, and therefore the philosophy which considers this kind of substance, will be first philosophy.

Also, check out the 8 tenets of River Forest / Aristotelian Thomism, which are elaborated in The Way toward Wisdom (vide the first chapter, this excerpt, John Deely's review) by Benedict Ashley, O.P., which discusses the question "What is metaphysics?"

The ultimate goal of the natural sciences is to show the existence of immaterial being(s).