Not all metal rusts, but the metals that do rust do so because of an oxidation reaction between the metal and water and oxygen. Oxidation is the process by which a substance incorporates oxygen into its molecular structure.
Iron is the metal most commonly associated with rust. Oxidated iron is called hydrated iron oxide, and it has the burnt orange color most commonly associated with rust. Copper also oxidizes, but the product is known as patina instead of rust; it takes on a green color rather than the orange associated with rusted iron. Aluminum, on the other hand, does not rust because its surface is made up of a natural layer of aluminum oxide, which prevents oxidation in the metal.