The way I understand it, Plato was some kind of a religious spelunker, who got lost in a cave and went mad.... Er, well actually his philosophy only sounds like the work of a religious madman lost in a dark cave. According to him, it is not shoes and chairs that are real, but rather the ideas of shoes and chairs that are "really" real. But that sounds nutty, so to confuse the issue, those ideas are called "forms" instead. (A frequent ploy in philosophy is to try to make goofy ideas sound more palatable by using a peculiar terminology.) To illustrate his theory he said you should imagine yourself to have spent your whole life chained in a cave, with your head restrained so that you cannot even look toward the light coming in the cave entrance. You can't see yourself or anybody or anything else. All you can see are the shadows of things on the wall at the back of the cave. In an analogous way, the things we take for real, such as people and houses and rocks and trees, are only "shadows" of the real things, the "forms", that lie behind them. Well that's the theory. You can believe it if you want; some people have, especially philosopher-types!
See also: IDEALISM