Aristotle believed that for something to be real it had to have a substance and a form or a body and a soul. Aristotle found no difference between matter and form, relying on nature to explain itself. He believed that each person can see form differently. What makes a table a table? The way Aristotle saw it was to look at fifty different tables and you would see what makes a table a table. He believed that form and matter can only be separated in a mental exercise, not in reality. He believed that in order to learn the forms of things we had to study and examine them. He saw that in our minds we can make the distinction between "tableness" and wood and then combine them both into a concept of a wooden table.
Form gives matter a structure to follow and matter gives form the stability. For example, wood is only a matter until the form of something gives it individual form and the form of something needing the matter to express itself. Now Plato on the other hand believed that reality is permanent and our senses can't be trusted. Plato maintains that there is a world of ideal forms, as we see material reflections of perfect forms.
He constructed a mathematical system of explaining processes. He believed in a theory of forms. That is, that there are perfect ways things should be that we as humans can see but can never achieve. For example, anyone knows what a perfect circle looks like, yet we can never draw an absolutely perfect circle. That's when Plato began to realize that "real" figures in geometry cannot be accurately or fully represented in this world.
While talking about forms of the circle we can then refer to Figure 2.1 on how each table in the world, in all different shapes and sizes can be considered a table because to a greater or lesser extent it is in a form of a table. What Plato was trying to express was that he believed that the form of a table existed in a world of perfects forms.