Rust is the common term for the oxidization of steel or iron, a chemical change caused by exposure to oxygen, frequently the oxygen in water. Rust appears as a brown or orange discolouration which can be scrubbed off. This discolouration can stain and damage fabric.
Silver is said to tarnish when it oxidizes, and can be re-polished to a high sheen.
Certain period metals such as lead and gold do not oxidize at all. Lead was therefore commonly used as a construction material (in particular to roof buildings) and gold was considered extremely valuable. Both these metals were too soft and heavy to be used as materials in armour, however.
The best defense against rust was (and is) keeping water from contacting the metal. In period, most metal armour was painted or left covered in forgeblack, rather than being polished. If armour was polished, it needed frequent scouring and oiling to maintain it.
Modern solutions to the problem of rust include stainless steel and galvanized steel, both of which resist (but are not proof against) oxidization. Aluminum is also resistant to oxidization is is sometimes used in SCA armour.