Metaphysics is the branch of philosophy dealing with the nature of reality: existence, identity, causation, matter, etc.
Being and existence are important enough topics in metaphysics that they eventually got their own specialized field of study: ontology. What things exist? What does it mean to exist - what qualities are shared by all things that exist? What kind of relations exist or can exist between things? (The exact relationship between metaphysics and ontology is, according to Wikipedia, “disputed”, but this is how I think about it.)