The corrosion of iron is specifically called rusting. Rusting occurs when iron reacts with oxygen and water (moisture) over time to form hydrated iron(III) oxide, commonly known as rust:
The iron(III) hydroxide gradually dehydrates to form the familiar reddish-brown rust (Fe2O3 . xH2O). Both oxygen and water must be present for rusting to occur; iron does not rust in dry air or in air-free water.
The other options are different processes entirely: burning (combustion) is a rapid reaction with oxygen involving flame and heat; galvanizing is a method of preventing corrosion by coating iron with a layer of zinc; alloying is mixing metals together to form an alloy (such as stainless steel), which is also a corrosion-prevention strategy, not a corrosion process.