Metaphysics derives its name from Aristotle's work. Following the treatise "Physics" came the book "Metaphysics", or "after physics". A large branch of metaphysics is "ontology". Ontology asks the question "what is?" The short answer is "everything". The long answer can fill a book.
Ontological commitments are what you must believe to exist if a given belief happens to be true. So if you believe that the past, present, and future are real, you are ontologically committed to a belief in time. If you believe in material beings, you are committed to a belief in matter.
Metaphysics intersects with ethics when we ask if humans have free will, or if all actions are determined by the previous state of the universe. Can we make meaningful choices, or do we not have control over our fate? Even if suppose that the chain of causality is completely mechanical, it might not be predictable enough for free will to be meaningless.
What is reality? Is the appearance of a thing to our senses sufficient to prove its existence? If something does not appear in any way, does that mean it is not real? It's the old question of "if a tree falls in a forest and nobody hears it, does it make a sound?" Bishop Berkeley argued esse est percipi ("to be is to be perceived"). He allowed for things to exist that are not perceived by humans by further arguing that all things are ideas in the eyes of God. Since God perceives everything, everything God perceives exists, and what God does not perceive does not exist. A parable tells us that when the acclaimed Dr. Johnson heard that Berkeley said that matter does not exist, he shouted "I refute it thus:" and stubbed his toe on a rock.
This leads us to the question of being, the heart of ontology. What is being like, in itself? Can we perceive it? Is there any mechanism for deciding the truth of our perception? Kant would argue that we cannot experience being-in-itself, but we can look at how our knowledge is formed and discover our ontological commitments. For example, to believe that things have bodies, we need to believe in space. We can discover the primordial requirements of experience, some a priori (deduced from theory rather than say, "a posteriori" discovered by experience) justification for a metaphysical fact.
Where do things come from? What causes things to be as they are? Such are questions that first require us to look at the metaphysical fact of causality. Is causality just something that we have observed over and over again, a posteriori, and concluded that every effect must have a cause by repetition, or is there an a priori foundation for causality? Aristotle broke causality (this question of why something is as it is) into four kinds: the material cause (the what), formal cause (the design), efficient cause (who or what made it), and final cause (the purpose). A piece of gum is materially made of sugars, formally made small enough for the mouth, efficiently processed by a machine, and finally made for mastication.
An old tale of causality. A lecturer is talking about the foundation of the world. A lady interjects and says, "what you are saying is nonsense. The world rests on the back of a giant turtle." To which the lecturer asks, "then what does the giant turtle rest on?" The lady replies, "on another, bigger, turtle, of course." And the lecturer replies, "what does that turtle rest on?" To which the lady says, "you can't trick me. It's turtles all the way down."
Either the universe is turtles all the way down, or there is some point -- some efficient cause -- from which all the other causes rest. This is called by Aristotle the First Cause. Also known as the Unmoved Mover, this is a version of the God explanation.
There are several explanations of the world that posit a God. I don't have space, time, or interest to revisit each of these. The weakest of these are about as interesting as the old Academic riddle "considering that angels do not have material bodies, how many angels can dance on the head of a pin?" The strongest is probably the Kalam cosmological argument: 1) everything that begins to exist has a cause; 2) the universe began to exist; therefore, 3) the universe has a cause. Unfortunately, this argument does not necessarily lead to the proof of the particular personal God that is common in my country. And secondly, it relies on a belief in causality that I do not believe has universal currency.
Particulars and universals. A particular is something we perceive: a red chair, a computer monitor, a cup of coffee. A universal is every instance of the perception. A red chair is a particular, but redness and chairness are universals. Plato argued that universals (what he called Forms) are real, and particulars simply borrow from reality. The opposite to this metaphysical realism is nominalism. This is the argument that the universal is merely a name, and the only thing that exists are the particulars behind the names. There is a difference between the sign and the signified. Signs only point to reality. If you point a finger at the moon and say "moon", a metaphysical realist might think that your finger is what you have meant by "moon".
These have parallels in Eastern philosophy. Causality is represented with the concept of "karma". The world of appearances is known as "samsara". And the recognition of reality is known as "nirvana" or "enlightenment".
Plato had a parable of enlightenment, known as the Parable of the Cave and found in his work “the Republic”. People are chained to the wall of a cave, only able to see shadows that move across the wall. They take these shadows to be the real world. A philosopher is someone who has broken free of their chains, climbed out of the cave, and seen the real world of sunlight, Plato's heaven of Forms. After seeing the world as it is, and comprehending the falsehoods believed by those who still live in the cave, the enlightened philosopher returns to free others.