Silver Coins are the standard currency in the world of Book of Heroes, earned by completing quests and defeating enemies. With them, you can buy all sorts of items in Majerio's Shop.
Gold Shields are the premium currency of Book of Heroes, and are much rarer throughout the world. Gold Shields will rarely drop off of enemies in combat. You can also purchase packs of them for real-world money.
Hero Tokens are used for Hero Training at the Training Hall. You can use Hero Tokens to permanently boost your stats. Hero Tokens are earned by completing feats, keeping Glenfort safe through the daily bounties, or you can exchange them for Gold Shields at Majerio’s shop.
Valor Tokens are earned by completing raids. The more raids you complete, the more valor you will earn. Different types of valor are awarded by completing different raids. Harder raids will award Valor that can be used to purchase higher level equipment. You can spend Valor tokens at Majerio’s shop for sigils, gems, and equipment.
Hero Score is just your score as a player. This is how you can compare yourself to other players on the leaderboard. Doing just about anything awards hero score, from defeating enemies to completing feats.