A universal is a kind of umbrella under which we put groups of individual things who share an essential quality or qualities. For example, all triangles have the feature of triangularity (three angles adding up to two right angles, etc.). So the question becomes, does this "triangularity" have any ontological status, such that it is an actual feature of reality, or is it just a name we give to a group of similar objects?
The realist position regarding Universals says that Universals themselves exist, in some substantial way. What that means is that a universal, say the form of a triangle or the color red, actually exists as a universal thing. Two examples of this position have been 1) Plato, whose theory of forms put forward the idea that Pure objects (triangularity, redness) exist separate from the particular instances of those objects (e.g.this
triangle, or a red shirt). Plato's theory was understandably rather primitive, and few still hold the position in exactly the way he put it forward. 2) Bertrand Russell is an example of a modern realist re: universals. He puts forth arguments supporting the idea that universals subsist independently of the spatialtemporal instances of them.
Nominalism states that universal entities of this kind (triangularity, redness) don't actually exist, but that they are only our classifications for a multiplicity of similarities, which we abstractly group together. This is more of an Aristotelian position (though not exactly), but the position is as ancient as philosophy itself. The modern analytic literature has all kinds of dumb names, like 'tropes' and things. But for good nominalist approaches one ought to look for Continental philosophers.