Stainless jewelry means that the metal is not prone to tarnish. A natural example would be brass, which is often more tarnish resistant than copper because it is alloyed with tin, a very shiny metal. Other examples are silver and gold, although these are expensive. An inexpensive but very attractive material to make jewelry with is stainless steel. It is twice as expensive as carbon steel, but it is cheaper than copper and definitely cheaper than silver. It does have a silvery sheen.
Made by alloying iron with chromium rather than carbon, this high grade steel is quite resistant to chemical tarnish, and it does not erode when subject to water and oxygen. This is just as well because jewelry is often worn on skin surfaces that tend to perspire when outdoors in warm weather. It does pay to polish chromium steel every now and then, but it really will not rust.