In Rune Factory 5, you can upgrade your armor by taking it to the blacksmith and using the appropriate materials. For example, to upgrade iron armor to steel armor, you will need iron ore and coal. The blacksmith will then use these materials to forge a new piece of armor for you.
You can also find armor upgrades in treasure chests or as rewards for completing quests. These upgrades are usually one-time use only, so be sure to use them wisely!