Metals differ greatly in how easily they give up electrons and thereby react with other substances. Iron gives up electrons relatively easily – it's considered a base metal.
In the presence of oxygen and moisture, iron therefore reacts step by step into iron oxide, which we know as rust. Unlike some other metals, this iron oxide doesn't form a protective, dense layer, but flakes off – so the reaction can keep advancing further into the metal.
Gold, on the other hand, holds onto its electrons very tightly and is considered a noble metal – under normal conditions, it practically doesn't react with oxygen or water. That's why gold stays shiny even after thousands of years, while unprotected iron rusts over time.