Plato’s Theory of Forms refers to an ideal version (which he called a Form or an Idea) of something of which all objects within the physical world are merely imitations of. The world a human being knows through his or her senses is only an imitation of the pure, eternal, and unchanging world of the Forms.
An example will help to illustrate Plato’s point. Consider a square. With the idea of a perfect square in mind, a person might try to sketch it on a piece of paper. However, the sketch would almost certainly turn out to be imperfect in some way (perhaps the sides aren’t even, or they are a bit skew), and will therefore be an inferior copy of the perfect square or Form of a Square. The Form Square simply refers to a perfect square that is perfect in all ways. Like the square, everything else in the world (circles, dogs, human beings, tables, trees, and concepts of justice, and beauty) are imperfect representations of their perfect Form. It is only the Form of Justice that is perfect justice, it is only the Form of Beauty that is perfect beauty, and it is only the Form of a Square that is a perfect square.
Plato went further than to settle with claim we only have the idea of a perfect form. He believed that Forms actually exist independently of the human mind. In other words, they are not just imaginative ideas within the mind but are imperceptible yet permanent, reliable, and unchangeable realities which structure the world and our knowledge of it. There are thus two different yet very real worlds: on the one hand there is the world of material things and then there’s the transcendent world of Ideas or Forms. For Plato, only those people who are able to recognize the Forms can comprehend the true reality behind the world of everyday experience, and therefore claim true and reliable knowledge of the world. Plato uses the example of a ruler who, in order to rule successfully, must recognize the Form of Goodness.
Perhaps Plato’s most famous example is his allegory of the cave in his Republic. Plato provides a scenario in which several captives are held chained to a wall within a cave. They have their backs to the cave’s mouth, and just behind them is a fire. Every time a object meets the fire it casts shadows onto the cave wall in front of the captives. The captives name these shadows for they perceive them to be reality. However, when some of the captives exit the cave they perceive reality anew by help from the sun. They then realize reality as they first perceived it from the shadows on the cave wall was not really reality at all. One of lessons of the analogy is that human beings are bound by a limited perception of reality from which they cannot break free. If people could break free they would experience another realm of reality which would be incomprehensible and beyond their understanding. This realm is what Plato believes is the pure Form of reality, of which human beings perceive only as an imperfect copy.