In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs both share the quality of "chairness", as well as greenness or the quality of being green; in other words, they share two "universals". There are three major kinds of qualities or characteristics: types or kinds (e.g. mammal), properties (e.g. short, strong), and relations (e.g. father of, next to). These are all different types of universals.
Paradigmatically, universals are abstract (e.g. humanity), whereas particulars are concrete (e.g. the personhood of Socrates). However, universals are not necessarily abstract and particulars are not necessarily concrete. For example, one might hold that numbers are particular yet abstract objects. Likewise, some philosophers, such as D. M. Armstrong, consider universals to be concrete.
Most do not consider classes to be universals, although some prominent philosophers do, such as John Bigelow.
Problem of universals
The problem of universals is an ancient problem in metaphysics about whether universals exist. The problem arises from attempts to account for the phenomenon of similarity or attribute agreement among things. For example, grass and Granny Smith apples are similar or agree in attribute, namely in having the attribute of greenness. The issue is how to account for this sort of agreement in attribute among things.
There are many philosophical positions regarding universals. Taking "beauty" as an example, four positions are:
Idealism: beauty is a property constructed in the mind, so it exists only in descriptions of things.
Platonic extreme realism: beauty is a property that exists in an ideal form independently of any mind or thing.
Aristotelian moderate realism or conceptualism: beauty is a property of things (fundamentum in re) that the mind abstracts from these beautiful things.