All Hero Armor provides a bonus which can give you an increased amount of Gold, Souls, and Experience from battles. A separate piece of Armor can be equipped for purely cosmetic reasons. Armor can be bought for Gems and as an In App-Purchase in the Hero menu found on the World Map.
The most sought-after sets are the Celestial Armor (+50% Gold, +100% Souls, +50% Experience) and Dragon Armor (+100% Gold, +50% Souls, +50% Experience) for 500 Gems each. There is also Deathknight Armor, a set that can only be purchased with real money. The bundle can be found in both the Armor Bonus tab in the Hero menu and in the Specials tab of the Shop (price may vary depending on location and platform).
You can equip the Armor by selecting a purchased set in the Armor Bonus or Style tabs of the Hero menu.
Note: Your Armor bonus is separate to your appearance. For example, you can have some of the best bonuses applied with Deathknight in the Armor Bonus tab, however, if you prefer the look of Dragon Armor you can have this selected to display on your Hero in the "Style" tab.
Note: Your Hero doesn't have to be in your team for you to use the Armor Bonus!