A red apple, a red car, and a red sunset have nothing physically in common beyond being, in each case, red. That word points to something they apparently share — a property philosophers call a universal, since it seems to apply generally across many distinct individual things (called particulars) rather than belonging to just one. The problem of universals asks a genuinely difficult metaphysical question about that apparent sharing: does redness exist as one single, real thing that each red object somehow participates in or instantiates, or is "redness" simply a convenient word applied after the fact to a collection of individually distinct particulars that merely resemble each other, with no single shared entity actually existing at all?
Realism says the universal genuinely exists
Realist positions on universals hold that properties like redness genuinely exist as real entities, not merely as words describing a pattern humans happen to notice. Platonic realism, tracing back to Plato's theory of Forms, holds that universals exist as abstract entities in their own right, independent of any particular red object and even independent of whether any red objects happen to exist at all. A more moderate realist position, associated with Aristotle, holds that universals are real but exist only within the particular things that instantiate them, rather than in some separate, independent abstract realm — redness is real, on this view, but only insofar as it's actually present in red things, not as a free-floating entity existing apart from them.
Nominalism denies the universal is anything more than a name
Nominalist positions take the opposite view: only individual particular things genuinely exist, and a general term like "red" is simply a convenient linguistic label applied to a collection of individually distinct objects that happen to resemble each other in a specific way, with no additional shared entity, abstract or otherwise, actually existing beyond the individual red things themselves and the resemblance between them. On this view, there's no single thing called "redness" that a red apple and a red sunset both somehow possess or participate in; there are simply many individual particular objects, some of which resemble each other closely enough that language groups them under a shared general term for convenience, without that convenience implying any further, additional metaphysical entity actually exists.
What we're still unsure about
That realist and nominalist positions on universals represent genuinely distinct, long-standing, and carefully worked-out metaphysical alternatives is well established in the history and current practice of philosophy, with sophisticated variants of each position still actively defended. What remains completely unresolved is which position, if either, is actually correct — the problem of universals is one of the longest-running open questions in metaphysics, stretching back to ancient Greek philosophy, and contemporary metaphysicians continue to develop new variants and arguments on both sides without anything resembling a settled, broadly accepted consensus answer.
This sits inside The Problem of Universals, one of seven topics in Metaphysics, one of five domains in Philosophy, one of seventeen subjects the app can quiz you on.