Nominalism posits that what is perceived is what exists in reality, whereas realists view a perceived object as the manifestation of a universal concept. Consequently, perception is not a one-to-one process of seeing something as it actually exists, but a synthesis of the underlying concept and real phenomena.
For nominalists, there are no universal concepts underlying reality, simply the phenomenon in front of us. Realists, on the other hand, maintain that all things that share the same property -- for example, greenness for all things with the color green -- are therefore linked by this property. Sharing this property implies possession of the same universal form. Realists further argue that for humans to have a conception of something in a generalized way, such as the idea of a cow without picturing a specific cow, there must be some underlying concept -- in this case, "cowness."
Realists maintain that for language to even exist, there must be some universal quality to phenomenon. To elaborate, human beings do not discuss each object as a completely independent, standalone entity to be analyzed but rather draw comparisons to other known objects to compile a series of properties to categorize it. Nominalists, on the other hand, while not denying that humans group things together by virtue of certain qualities, maintain that this is simply a convention of language based on people's perception of them. Just because two objects share the same perceptible quality does not necessarily warrant grouping them together in any real way; it's simply a human way of making sense of reality through the senses.
The most famous nominalist was the ancient Greek philosopher Plato. Plato was the first to argue that there was a realm of ideas separate from perceptible reality from which all ideas, or forms, came. Later nominalists included Immanuel Kant, who posited his theory of empirical realism. For Kant, there could be no mind-independent view of the world as nominalists would hold since there are certain inherent logical structures within the mind that constrain perception. Nominalism came as a response to realists and was furthered by thinkers such as William of Ockham, George Berkeley and David Hume.