Explain how painting of an iron gate prevents it from rusting

Rust is a film of brownish substance, which is produced on iron substances when exposed to moist air (which contains both oxygen and water). 

The oxygen and water in the air react with the iron to form iron oxide.

$\mathrm{Iron} \left(\mathrm{Fe}\right) + \mathrm{Oxygen} ({\mathrm{O}}_2, \mathrm{from} \mathrm{the} \mathrm{air}) + \mathrm{water} \left({\mathrm{H}}_2\mathrm{O}\right) \to \mathrm{rust} (\mathrm{iron} \mathrm{oxide} {\mathrm{Fe}}_2{\mathrm{O}}_3)$

When the iron gate is painted, it protects the iron from coming into contact with oxygen and moisture. Hence, it prevents it from rusting.