"Gems are used for many things, like buying heroes from the Rare Summon, speeding up chest unlocks, and getting more energy. You can get gems by completing quests or buying more in the shop.
Gold is needed for upgrading and evolving your heroes and upgrading your fort. Get more gold from chests or by selling heroes. Golden heroes give more gold than regular heroes when you sell them. The best places to capture golden heroes are the Golden Creatures event once a week and the Portal Key dungeon Bug Paradise.
Honor is used for summoning heroes. You get honor either by completing Quests, or when your friends use your leader hero as their reinforcement when they play a dungeon. This means you need friends to get Honor! To make friends, you can send friend invitations; all you need to do is go to a dungeon, select a reinforcement who is not yet your friend, complete the dungeon, and a dialog asking you to send a request will appear. You can see your friends and the friend requests you receive from other players in the Guild tab under Friends.