To tarnish is to become dull or discolored. Silver tends to tarnish easily, which is why your mother is always having you polish the family silver.
As a noun, a tarnish is the dull layer of corrosion that sometimes forms on metal items, usually the result of the metal reacting to oxygen in the air. Metals are most likely to tarnish, but so can anything that once felt sparkly and bright but has lost its luster — even you. If the new kid just beat you in chess, your reputation as the best chess player in your class has started to tarnish. Better not lose again!