Speaking literally (or at least etymologically) metaphysics refers to 'that which goes beyond physics (the material aspects of the world and the body)'. This includes theology, but also extends to things like being-ness, identity, subjective experience and qualia, intersubjectivity, universal abstractions, and other things that are seemingly indivisible essences or first principles. Certain concepts in physics — e.g. the fundamental forces and particles of the Standard Model — are perhaps best thought of as metaphysical concepts since they aren't themselves subject to direct experiences but are instead presupposed as an explanation for secondary observations.
For Aristotle, metaphysics was itself a science that went beyond the 'practical' science of measuring and manipulating material substances. Modern empiricism tends to restrict the term 'science' to purely material activities, so metaphysics is cast as a logic or philosophy, not a science per se. But that does't imply that metaphysics is necessarily less rigorous than physical science, merely that it's less focused on empirical outcomes.
The question "What am I made of?" is a matter for physics. The question "What am I physically?" is a matter for biology. But the question "Who am I? is intractably a matter for metaphysics. One cannot answer the last using the tools and methods of the first two.