Universals answer the question of how one can look at an object and identify it with out being told what it is? For instance, chairs come is all shapes, sizes, materials, and colors and yet when I see a chair, I know it's a chair. How is that possible when the variations can be staggering? According to Plato, I must already have a vague idea of what makes a chair a chair. This is Plato's theory of the Forms (Google: Allegory of the cave, to read about Plato's concept).
Forms are eternal, unchanging realities from which everything gets it's essential identity. They are the transcendental blueprint which, to Plato, are more real than the object that participates in it's likeness. Everyone has a "knowledge" of these Forms, but it's a knowledge like only knowing an object by it's shadow.
For instance, there is a Form of what it means to be human. All humans share in correspondence to that Form, no matter how different those people are, they are people based on that "blueprint".
Neo-Platonism arrived around the time of Christ and they postulated about the One: an oblivious, eternal entity who is Mind, from which everything in necessarily created. This Mind is what conceives of the Universals (which used to be Forms).
The Church Fathers, seeing the obvious similarities between Neo-Platonism and Christianity picked up on this idea of God as Mind and thoroughly adapted it to a Christian worldview. The One is replaced with the Christian God: an eternal and relational being who creates out of his own will rather than by necessity. The Mind of God holds the Universals and they have real existence.
Next up: Why Nominalism Matters to You!