For more information on origami, visit Origami USA.
Simply put, origami is the art of folding paper. Invented in China (paper was invented in China), origami was popularized in Japan and has been associated with Japanese culture for hundreds of years.
Traditional purist origami requires folding from a single uncut square. No cutting, no ripping, no tearing, no gluing, no taping, no nothing but folding.
Kiragami is the art of cutting paper. Modular origami involves folding several individual units and joining them together through locking folds to create a single model, such as an ornament or rider on horseback (though most purists prefer the challenge of creating figures like this in the purist tradition of using an uncut square).
Grab some paper and buy a book on origami. John Montroll has a number of books that are excellent for a beginner and experts alike.