Gold is one of the currencies in the game.
Gold is earned as rewards for clearing levels while exploring, for completing various Quests, Events, etc. The most significant ways to acquire gold is via the Gold Trial, Angel Trial, and some Guild activities. Gold can also be purchased in exchange for Diamonds.
Gold is likely to be your most valuable resource and a limiting factor in your progression. You will be less frustrated overall if you consider the benefit of spending gold on any particular item / upgrade. In particular, GT Arcade likes to have events where you are rewarded for spending gold in the shops, etc. Be careful about pursuing this as the overall benefit of the Event reward may not be as valuable as if you'd spent your gold on advancing your Hero's Runes or Relics.